{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<!--NAVIGATION-->\n",
"< | [Main Contents](https://vectorbite.github.io/VBiTraining2/) | >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Model Fitting in (Vector-Borne Disease) Ecology and Evolution <span class=\"tocSkip\">"
]
},
{
"cell_type": "markdown",
"metadata": {
"toc": true
},
"source": [
"<h1>Contents<span class=\"tocSkip\"></span></h1>\n",
"<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Introduction\" data-toc-modified-id=\"Introduction-1\"><span class=\"toc-item-num\">1 </span>Introduction</a></span></li><li><span><a href=\"#Model-fitting-using-Non-linear-least-squares\" data-toc-modified-id=\"Model-fitting-using-Non-linear-least-squares-2\"><span class=\"toc-item-num\">2 </span>Model fitting using Non-linear least squares</a></span><ul class=\"toc-item\"><li><span><a href=\"#Traits-data-as-an-example\" data-toc-modified-id=\"Traits-data-as-an-example-2.1\"><span class=\"toc-item-num\">2.1 </span>Traits data as an example</a></span></li><li><span><a href=\"#Allometric-scaling-of-traits\" data-toc-modified-id=\"Allometric-scaling-of-traits-2.2\"><span class=\"toc-item-num\">2.2 </span>Allometric scaling of traits</a></span><ul class=\"toc-item\"><li><span><a href=\"#Exercises-\" data-toc-modified-id=\"Exercises--2.2.1\"><span class=\"toc-item-num\">2.2.1 </span>Exercises <a id=\"Allom_Exercises\"></a></a></span></li><li><span><a href=\"#Comparing-models\" data-toc-modified-id=\"Comparing-models-2.2.2\"><span class=\"toc-item-num\">2.2.2 </span>Comparing models</a></span></li><li><span><a href=\"#Exercises-\" data-toc-modified-id=\"Exercises--2.2.3\"><span class=\"toc-item-num\">2.2.3 </span>Exercises <a id=\"ModelSelection_Exercises\"></a></a></span></li></ul></li><li><span><a href=\"#Albatross-chick-growth\" data-toc-modified-id=\"Albatross-chick-growth-2.3\"><span class=\"toc-item-num\">2.3 </span>Albatross chick growth</a></span><ul class=\"toc-item\"><li><span><a href=\"#Fitting-the-three-models-using-NLLS\" data-toc-modified-id=\"Fitting-the-three-models-using-NLLS-2.3.1\"><span class=\"toc-item-num\">2.3.1 </span>Fitting the three models using NLLS</a></span></li><li><span><a href=\"#Exercises-\" data-toc-modified-id=\"Exercises--2.3.2\"><span class=\"toc-item-num\">2.3.2 </span>Exercises <a id=\"Albatross_Exercises\"></a></a></span></li></ul></li><li><span><a href=\"#Aedes-aegypti-fecundity\" data-toc-modified-id=\"Aedes-aegypti-fecundity-2.4\"><span class=\"toc-item-num\">2.4 </span>Aedes aegypti fecundity</a></span><ul class=\"toc-item\"><li><span><a href=\"#The-TPC-models\" data-toc-modified-id=\"The-TPC-models-2.4.1\"><span class=\"toc-item-num\">2.4.1 </span>The TPC models</a></span></li><li><span><a href=\"#Exercises-\" data-toc-modified-id=\"Exercises--2.4.2\"><span class=\"toc-item-num\">2.4.2 </span>Exercises <a id=\"Aedes_Exercises\"></a></a></span></li></ul></li><li><span><a href=\"#Abundances-as-an-example\" data-toc-modified-id=\"Abundances-as-an-example-2.5\"><span class=\"toc-item-num\">2.5 </span>Abundances as an example</a></span><ul class=\"toc-item\"><li><span><a href=\"#Why-Abundances?\" data-toc-modified-id=\"Why-Abundances?-2.5.1\"><span class=\"toc-item-num\">2.5.1 </span>Why Abundances?</a></span></li><li><span><a href=\"#Population-growth-rate-example\" data-toc-modified-id=\"Population-growth-rate-example-2.5.2\"><span class=\"toc-item-num\">2.5.2 </span>Population growth rate example</a></span></li><li><span><a href=\"#Exercises\" data-toc-modified-id=\"Exercises-2.5.3\"><span class=\"toc-item-num\">2.5.3 </span>Exercises</a></span></li></ul></li><li><span><a href=\"#Model-fitting-using-Maximum-Likelihood\" data-toc-modified-id=\"Model-fitting-using-Maximum-Likelihood-2.6\"><span class=\"toc-item-num\">2.6 </span>Model fitting using Maximum Likelihood</a></span><ul class=\"toc-item\"><li><span><a href=\"#Implementing-the-Likelihood-in-R\" data-toc-modified-id=\"Implementing-the-Likelihood-in-R-2.6.1\"><span class=\"toc-item-num\">2.6.1 </span>Implementing the Likelihood in R</a></span></li><li><span><a href=\"#Likelihood-profile-in-R\" data-toc-modified-id=\"Likelihood-profile-in-R-2.6.2\"><span class=\"toc-item-num\">2.6.2 </span>Likelihood profile in R</a></span></li><li><span><a href=\"#Likelihood-surface-in-R\" data-toc-modified-id=\"Likelihood-surface-in-R-2.6.3\"><span class=\"toc-item-num\">2.6.3 </span>Likelihood surface in R</a></span></li><li><span><a href=\"#Conditional-Likelihood\" data-toc-modified-id=\"Conditional-Likelihood-2.6.4\"><span class=\"toc-item-num\">2.6.4 </span>Conditional Likelihood</a></span></li><li><span><a href=\"#Alternatives-to-Grid-Search\" data-toc-modified-id=\"Alternatives-to-Grid-Search-2.6.5\"><span class=\"toc-item-num\">2.6.5 </span>Alternatives to Grid Search</a></span></li><li><span><a href=\"#Maximum-Likelihood-using-optim()\" data-toc-modified-id=\"Maximum-Likelihood-using-optim()-2.6.6\"><span class=\"toc-item-num\">2.6.6 </span>Maximum Likelihood using <code>optim()</code></a></span></li><li><span><a href=\"#Confidence-intervals\" data-toc-modified-id=\"Confidence-intervals-2.6.7\"><span class=\"toc-item-num\">2.6.7 </span>Confidence intervals</a></span></li><li><span><a href=\"#Comparison-to-fitting-with-least-squares\" data-toc-modified-id=\"Comparison-to-fitting-with-least-squares-2.6.8\"><span class=\"toc-item-num\">2.6.8 </span>Comparison to fitting with least squares</a></span></li><li><span><a href=\"#Model-Selection\" data-toc-modified-id=\"Model-Selection-2.6.9\"><span class=\"toc-item-num\">2.6.9 </span>Model Selection</a></span></li><li><span><a href=\"#Exercises-\" data-toc-modified-id=\"Exercises--2.6.10\"><span class=\"toc-item-num\">2.6.10 </span>Exercises <a id=\"MLE_Exercises\"></a></a></span></li></ul></li></ul></li><li><span><a href=\"#Fitting-Models-the-Bayesian-way\" data-toc-modified-id=\"Fitting-Models-the-Bayesian-way-3\"><span class=\"toc-item-num\">3 </span>Fitting Models the Bayesian way</a></span><ul class=\"toc-item\"><li><ul class=\"toc-item\"><li><span><a href=\"#A-Likelihoods-exercise\" data-toc-modified-id=\"A-Likelihoods-exercise-3.0.1\"><span class=\"toc-item-num\">3.0.1 </span>A Likelihoods exercise</a></span><ul class=\"toc-item\"><li><span><a href=\"#The-Binomial-Distribution\" data-toc-modified-id=\"The-Binomial-Distribution-3.0.1.1\"><span class=\"toc-item-num\">3.0.1.1 </span>The Binomial Distribution</a></span></li><li><span><a href=\"#Method-of-Moments-(MoM)-Estimators\" data-toc-modified-id=\"Method-of-Moments-(MoM)-Estimators-3.0.1.2\"><span class=\"toc-item-num\">3.0.1.2 </span>Method of Moments (MoM) Estimators</a></span></li><li><span><a href=\"#MLE-for-Binomial-Distribution\" data-toc-modified-id=\"MLE-for-Binomial-Distribution-3.0.1.3\"><span class=\"toc-item-num\">3.0.1.3 </span>MLE for Binomial Distribution</a></span></li><li><span><a href=\"#Computing-the-likelihood-and-MLE-in-R\" data-toc-modified-id=\"Computing-the-likelihood-and-MLE-in-R-3.0.1.4\"><span class=\"toc-item-num\">3.0.1.4 </span>Computing the likelihood and MLE in R</a></span></li></ul></li></ul></li><li><span><a href=\"#Example:-Midge-Wing-Length\" data-toc-modified-id=\"Example:-Midge-Wing-Length-3.1\"><span class=\"toc-item-num\">3.1 </span>Example: Midge Wing Length</a></span><ul class=\"toc-item\"><li><span><a href=\"#Non-Bayesian-analysis\" data-toc-modified-id=\"Non-Bayesian-analysis-3.1.1\"><span class=\"toc-item-num\">3.1.1 </span>Non-Bayesian analysis</a></span></li><li><span><a href=\"#Setting-up-the-Bayesian-Model\" data-toc-modified-id=\"Setting-up-the-Bayesian-Model-3.1.2\"><span class=\"toc-item-num\">3.1.2 </span>Setting up the Bayesian Model</a></span><ul class=\"toc-item\"><li><span><a href=\"#Prior-Information\" data-toc-modified-id=\"Prior-Information-3.1.2.1\"><span class=\"toc-item-num\">3.1.2.1 </span>Prior Information</a></span></li></ul></li><li><span><a href=\"#Analytic-Posterior\" data-toc-modified-id=\"Analytic-Posterior-3.1.3\"><span class=\"toc-item-num\">3.1.3 </span>Analytic Posterior</a></span></li><li><span><a href=\"#Exercise:-Prior-sensitivity\" data-toc-modified-id=\"Exercise:-Prior-sensitivity-3.1.4\"><span class=\"toc-item-num\">3.1.4 </span>Exercise: Prior sensitivity</a></span></li><li><span><a href=\"#Numerical-evaluation-of-the-posterior-with-JAGS\" data-toc-modified-id=\"Numerical-evaluation-of-the-posterior-with-JAGS-3.1.5\"><span class=\"toc-item-num\">3.1.5 </span>Numerical evaluation of the posterior with JAGS</a></span><ul class=\"toc-item\"><li><span><a href=\"#Specifying-the-model\" data-toc-modified-id=\"Specifying-the-model-3.1.5.1\"><span class=\"toc-item-num\">3.1.5.1 </span>Specifying the model</a></span></li></ul></li><li><span><a href=\"#Estimating-the-population-variance\" data-toc-modified-id=\"Estimating-the-population-variance-3.1.6\"><span class=\"toc-item-num\">3.1.6 </span>Estimating the population variance</a></span></li><li><span><a href=\"#Exercise:-Updating-the-Bayesian-model\" data-toc-modified-id=\"Exercise:-Updating-the-Bayesian-model-3.1.7\"><span class=\"toc-item-num\">3.1.7 </span>Exercise: Updating the Bayesian model</a></span></li><li><span><a href=\"#Aedes-data-revisited-using-Bayesian-fitting\" data-toc-modified-id=\"Aedes-data-revisited-using-Bayesian-fitting-3.1.8\"><span class=\"toc-item-num\">3.1.8 </span>Aedes data revisited using Bayesian fitting</a></span><ul class=\"toc-item\"><li><span><a href=\"#The-Data\" data-toc-modified-id=\"The-Data-3.1.8.1\"><span class=\"toc-item-num\">3.1.8.1 </span>The Data</a></span></li><li><span><a href=\"#Two-thermal-performance-curve-models\" data-toc-modified-id=\"Two-thermal-performance-curve-models-3.1.8.2\"><span class=\"toc-item-num\">3.1.8.2 </span>Two thermal performance curve models</a></span></li><li><span><a href=\"#The-thermal-response-model-file\" data-toc-modified-id=\"The-thermal-response-model-file-3.1.8.3\"><span class=\"toc-item-num\">3.1.8.3 </span>The thermal response model file</a></span></li><li><span><a href=\"#Running-diagnostics\" data-toc-modified-id=\"Running-diagnostics-3.1.8.4\"><span class=\"toc-item-num\">3.1.8.4 </span>Running diagnostics</a></span></li><li><span><a href=\"#Plot-the-fits\" data-toc-modified-id=\"Plot-the-fits-3.1.8.5\"><span class=\"toc-item-num\">3.1.8.5 </span>Plot the fits</a></span></li><li><span><a href=\"#Additional-analyses\" data-toc-modified-id=\"Additional-analyses-3.1.8.6\"><span class=\"toc-item-num\">3.1.8.6 </span>Additional analyses</a></span></li></ul></li><li><span><a href=\"#A-Bayesian-model-fitting-of-abundance-data\" data-toc-modified-id=\"A-Bayesian-model-fitting-of-abundance-data-3.1.9\"><span class=\"toc-item-num\">3.1.9 </span>A Bayesian model fitting of abundance data</a></span><ul class=\"toc-item\"><li><span><a href=\"#The-Data\" data-toc-modified-id=\"The-Data-3.1.9.1\"><span class=\"toc-item-num\">3.1.9.1 </span>The Data</a></span></li><li><span><a href=\"#Specifying-the-growth-curve\" data-toc-modified-id=\"Specifying-the-growth-curve-3.1.9.2\"><span class=\"toc-item-num\">3.1.9.2 </span>Specifying the growth curve</a></span></li><li><span><a href=\"#The-thermal-response-model-file\" data-toc-modified-id=\"The-thermal-response-model-file-3.1.9.3\"><span class=\"toc-item-num\">3.1.9.3 </span>The thermal response model file</a></span></li><li><span><a href=\"#Additional-settings-for-jags\" data-toc-modified-id=\"Additional-settings-for-jags-3.1.9.4\"><span class=\"toc-item-num\">3.1.9.4 </span>Additional settings for jags</a></span></li><li><span><a href=\"#Fitting-the-model\" data-toc-modified-id=\"Fitting-the-model-3.1.9.5\"><span class=\"toc-item-num\">3.1.9.5 </span>Fitting the model</a></span></li><li><span><a href=\"#Diagnostics\" data-toc-modified-id=\"Diagnostics-3.1.9.6\"><span class=\"toc-item-num\">3.1.9.6 </span>Diagnostics</a></span></li><li><span><a href=\"#Visualizing-the-joint-posterior-of-parameters\" data-toc-modified-id=\"Visualizing-the-joint-posterior-of-parameters-3.1.9.7\"><span class=\"toc-item-num\">3.1.9.7 </span>Visualizing the joint posterior of parameters</a></span></li><li><span><a href=\"#The-posterior-distribution-of-the-mean-function\" data-toc-modified-id=\"The-posterior-distribution-of-the-mean-function-3.1.9.8\"><span class=\"toc-item-num\">3.1.9.8 </span>The posterior distribution of the mean function</a></span></li></ul></li></ul></li><li><span><a href=\"#Readings-and-Resources-\" data-toc-modified-id=\"Readings-and-Resources--3.2\"><span class=\"toc-item-num\">3.2 </span>Readings and Resources <a id=\"Readings\"></a></a></span></li></ul></li></ul></div>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Introduction\n",
"\n",
"This notebook assumes that you have already seen the [lecture](https://github.com/vectorbite/VBiTraining2/blob/master/lectures/ModelFitting) on model fitting in Ecology and Evolution. In this workshop we will work through multiple techniques to do so using various examples."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"# For starters, clear all variables and graphic devices and load necessary packages:\n",
"\n",
"rm(list = ls())\n",
"graphics.off()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"library(repr)\n",
"options(repr.plot.width=5, repr.plot.height=4) # Change default plot size; not necessary if you are using Rstudio"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Model fitting using Non-linear least squares\n",
"\n",
"We will work with several practical examples here. These assume that you have at least a conceptual understanding of what Linear vs Non-linear models are, how they are fitted to data, and how the fits can be assessed statistically. If not, you may want to see the [Linear Models](https://github.com/vectorbite/VBiTraining2/blob/master/lectures/LinearModels) ([video here](https://drive.google.com/drive/folders/12Sj56wHX6vcAnp9GE9qQ1gIXbn7QRHU2?usp=sharing)) and [NLLS](https://github.com/mhasoba/TheMulQuaBio/blob/master/lectures/NLLS) lectures first.\n",
"\n",
"You will need the `nls.lm` R package, which you can install using the standard method (linux users, launch R in `sudo` mode first):\n",
"\n",
"```r\n",
"> install.packages(\"minpack.lm\") \n",
"```\n",
"\n",
"*Why `nls.lm`*? The standard NLLS function in R, called `nls`, uses a less robust algorithm called the Gauss-Newton algorithm. Therefore, `nls` will often fail to fit your model to the data if you start off at starting values for the parameters that are too far from what the optimal values would be, especially if the \"parameter space\" is weirdly shaped, i.e., the model has a mathematical form that makes it hard to find parameter combinations that minimize the residual sum of squared (RSS). If this does not makes sense, don't worry about it- just go with `nls_LM` from the `nls.lm` package instead of `nls`! If you are really curious, try substituting `nls` for `nls_LM` in the examples below and compare the results.\n",
"\n",
"Now load the `minpack.lm` package:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"run_control": {
"marked": true
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Loading required package: minpack.lm\n"
]
}
],
"source": [
"require(\"minpack.lm\") # for Levenberg-Marquardt nlls fitting"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Traits data as an example \n",
"\n",
"Our first set of examples will focus on traits. \n",
"\n",
"A trait is any measurable feature of an individual organism. This includes physical traits (e.g., morphology, body mass, wing length), performance traits (e.g., respiration rate, body velocity, fecundity), and behavioral traits (e.g., feeding preference, foraging strategy, mate choice). All natural populations show variation in traits across individuals. A trait is functional when it directly (e.g., mortality rate) or indirectly (e.g., somatic development or growth rate) determines individual fitness. Therefore, variation in (functional) traits can generate variation in the rate of increase and persistence of populations. When measured in the context of life cycles, without considering interactions with other organisms (e.g., predators or prey of the vector), functional traits are typically called life history traits (such as mortality rate and fecundity). Other traits determine interactions both within the vector population (e.g., intra-specific interference or mating frequency) and between vectors and other species, including the species which may act as resources (prey, for example). Thus both life history and interaction traits determine vector population fitness and therefore abundance, which ultimately influences disease transmission rate. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Allometric scaling of traits\n",
"\n",
"Let's start with a common and reasonably simple example from biology: [allometric scaling](https://en.wikipedia.org/wiki/Allometry). Allometric relationships between linear measurements such as body length, wing span, and thorax width are a good way to obtain estimates of body weights of individual vectors such as mosquitoes, ticks, and flies. We will look at allometric scaling of body weight vs. total body length in dragonflies and damselfiles (yes, these are not known vectors!). \n",
"\n",
"Allometric relationships take the form:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a id='eq:allom'></a>\n",
"$$\n",
"y = a x^b\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"where $x$ and $y$ are morphological measures (body length and body weight respectively, in our current example), the constant is the value of $y$ at body length $x = 1$ unit, and $b$ is the scaling \"exponent\". This is also called a power-law, because $y$ relates to $x$ through a simple power. \n",
"\n",
"First create a function object for the power law model:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"powMod <- function(x, a, b) {\n",
" return(a * x^b)\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now get the [data](https://raw.githubusercontent.com/mhasoba/TheMulQuaBio/master/data/GenomeSize.csv) (first click on link and use \"Save as\" or `Ctrl+S` to download it as a csv). Then, save it in your `data` directory. After that, import it into your R workspace:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/html": [
"<table>\n",
"<thead><tr><th scope=col>Suborder</th><th scope=col>Family</th><th scope=col>Species</th><th scope=col>GenomeSize</th><th scope=col>GenomeSE</th><th scope=col>GenomeN</th><th scope=col>BodyWeight</th><th scope=col>TotalLength</th><th scope=col>HeadLength</th><th scope=col>ThoraxLength</th><th scope=col>AdbdomenLength</th><th scope=col>ForewingLength</th><th scope=col>HindwingLength</th><th scope=col>ForewingArea</th><th scope=col>HindwingArea</th><th scope=col>MorphologyN</th></tr></thead>\n",
"<tbody>\n",
"\t<tr><td>Anisoptera </td><td>Aeshnidae </td><td>Aeshna canadensis </td><td>2.20 </td><td> NA </td><td>1 </td><td>0.159 </td><td>67.58 </td><td>6.83 </td><td>11.81 </td><td>48.94 </td><td>45.47 </td><td>45.40 </td><td>369.57 </td><td>483.61 </td><td>2 </td></tr>\n",
"\t<tr><td>Anisoptera </td><td>Aeshnidae </td><td>Aeshna constricta </td><td>1.76 </td><td>0.06 </td><td>4 </td><td>0.228 </td><td>71.97 </td><td>6.84 </td><td>10.72 </td><td>54.41 </td><td>46.00 </td><td>45.48 </td><td>411.15 </td><td>517.38 </td><td>3 </td></tr>\n",
"\t<tr><td>Anisoptera </td><td>Aeshnidae </td><td>Aeshna eremita </td><td>1.85 </td><td> NA </td><td>1 </td><td>0.312 </td><td>78.80 </td><td>6.27 </td><td>16.19 </td><td>56.33 </td><td>51.24 </td><td>49.47 </td><td>460.72 </td><td>574.33 </td><td>1 </td></tr>\n",
"\t<tr><td>Anisoptera </td><td>Aeshnidae </td><td>Aeshna tuberculifera</td><td>1.78 </td><td>0.10 </td><td>2 </td><td>0.218 </td><td>72.44 </td><td>6.62 </td><td>12.53 </td><td>53.29 </td><td>49.84 </td><td>48.82 </td><td>468.74 </td><td>591.42 </td><td>2 </td></tr>\n",
"\t<tr><td>Anisoptera </td><td>Aeshnidae </td><td>Aeshna umbrosa </td><td>2.00 </td><td> NA </td><td>1 </td><td>0.207 </td><td>73.05 </td><td>4.92 </td><td>11.11 </td><td>57.03 </td><td>46.51 </td><td>45.97 </td><td>382.48 </td><td>481.44 </td><td>1 </td></tr>\n",
"\t<tr><td>Anisoptera </td><td>Aeshnidae </td><td>Aeshna verticalis </td><td>1.59 </td><td> NA </td><td>1 </td><td>0.220 </td><td>66.25 </td><td>6.48 </td><td>11.64 </td><td>48.13 </td><td>45.91 </td><td>44.91 </td><td>400.40 </td><td>486.97 </td><td>1 </td></tr>\n",
"</tbody>\n",
"</table>\n"
],
"text/latex": [
"\\begin{tabular}{r|llllllllllllllll}\n",
" Suborder & Family & Species & GenomeSize & GenomeSE & GenomeN & BodyWeight & TotalLength & HeadLength & ThoraxLength & AdbdomenLength & ForewingLength & HindwingLength & ForewingArea & HindwingArea & MorphologyN\\\\\n",
"\\hline\n",
"\t Anisoptera & Aeshnidae & Aeshna canadensis & 2.20 & NA & 1 & 0.159 & 67.58 & 6.83 & 11.81 & 48.94 & 45.47 & 45.40 & 369.57 & 483.61 & 2 \\\\\n",
"\t Anisoptera & Aeshnidae & Aeshna constricta & 1.76 & 0.06 & 4 & 0.228 & 71.97 & 6.84 & 10.72 & 54.41 & 46.00 & 45.48 & 411.15 & 517.38 & 3 \\\\\n",
"\t Anisoptera & Aeshnidae & Aeshna eremita & 1.85 & NA & 1 & 0.312 & 78.80 & 6.27 & 16.19 & 56.33 & 51.24 & 49.47 & 460.72 & 574.33 & 1 \\\\\n",
"\t Anisoptera & Aeshnidae & Aeshna tuberculifera & 1.78 & 0.10 & 2 & 0.218 & 72.44 & 6.62 & 12.53 & 53.29 & 49.84 & 48.82 & 468.74 & 591.42 & 2 \\\\\n",
"\t Anisoptera & Aeshnidae & Aeshna umbrosa & 2.00 & NA & 1 & 0.207 & 73.05 & 4.92 & 11.11 & 57.03 & 46.51 & 45.97 & 382.48 & 481.44 & 1 \\\\\n",
"\t Anisoptera & Aeshnidae & Aeshna verticalis & 1.59 & NA & 1 & 0.220 & 66.25 & 6.48 & 11.64 & 48.13 & 45.91 & 44.91 & 400.40 & 486.97 & 1 \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"Suborder | Family | Species | GenomeSize | GenomeSE | GenomeN | BodyWeight | TotalLength | HeadLength | ThoraxLength | AdbdomenLength | ForewingLength | HindwingLength | ForewingArea | HindwingArea | MorphologyN | \n",
"|---|---|---|---|---|---|\n",
"| Anisoptera | Aeshnidae | Aeshna canadensis | 2.20 | NA | 1 | 0.159 | 67.58 | 6.83 | 11.81 | 48.94 | 45.47 | 45.40 | 369.57 | 483.61 | 2 | \n",
"| Anisoptera | Aeshnidae | Aeshna constricta | 1.76 | 0.06 | 4 | 0.228 | 71.97 | 6.84 | 10.72 | 54.41 | 46.00 | 45.48 | 411.15 | 517.38 | 3 | \n",
"| Anisoptera | Aeshnidae | Aeshna eremita | 1.85 | NA | 1 | 0.312 | 78.80 | 6.27 | 16.19 | 56.33 | 51.24 | 49.47 | 460.72 | 574.33 | 1 | \n",
"| Anisoptera | Aeshnidae | Aeshna tuberculifera | 1.78 | 0.10 | 2 | 0.218 | 72.44 | 6.62 | 12.53 | 53.29 | 49.84 | 48.82 | 468.74 | 591.42 | 2 | \n",
"| Anisoptera | Aeshnidae | Aeshna umbrosa | 2.00 | NA | 1 | 0.207 | 73.05 | 4.92 | 11.11 | 57.03 | 46.51 | 45.97 | 382.48 | 481.44 | 1 | \n",
"| Anisoptera | Aeshnidae | Aeshna verticalis | 1.59 | NA | 1 | 0.220 | 66.25 | 6.48 | 11.64 | 48.13 | 45.91 | 44.91 | 400.40 | 486.97 | 1 | \n",
"\n",
"\n"
],
"text/plain": [
" Suborder Family Species GenomeSize GenomeSE GenomeN\n",
"1 Anisoptera Aeshnidae Aeshna canadensis 2.20 NA 1 \n",
"2 Anisoptera Aeshnidae Aeshna constricta 1.76 0.06 4 \n",
"3 Anisoptera Aeshnidae Aeshna eremita 1.85 NA 1 \n",
"4 Anisoptera Aeshnidae Aeshna tuberculifera 1.78 0.10 2 \n",
"5 Anisoptera Aeshnidae Aeshna umbrosa 2.00 NA 1 \n",
"6 Anisoptera Aeshnidae Aeshna verticalis 1.59 NA 1 \n",
" BodyWeight TotalLength HeadLength ThoraxLength AdbdomenLength ForewingLength\n",
"1 0.159 67.58 6.83 11.81 48.94 45.47 \n",
"2 0.228 71.97 6.84 10.72 54.41 46.00 \n",
"3 0.312 78.80 6.27 16.19 56.33 51.24 \n",
"4 0.218 72.44 6.62 12.53 53.29 49.84 \n",
"5 0.207 73.05 4.92 11.11 57.03 46.51 \n",
"6 0.220 66.25 6.48 11.64 48.13 45.91 \n",
" HindwingLength ForewingArea HindwingArea MorphologyN\n",
"1 45.40 369.57 483.61 2 \n",
"2 45.48 411.15 517.38 3 \n",
"3 49.47 460.72 574.33 1 \n",
"4 48.82 468.74 591.42 2 \n",
"5 45.97 382.48 481.44 1 \n",
"6 44.91 400.40 486.97 1 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"MyData <- read.csv(\"../data/GenomeSize.csv\")\n",
"\n",
"head(MyData)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Anisoptera](https://en.wikipedia.org/wiki/Dragonfly) are dragonflies, and [Zygoptera](https://en.wikipedia.org/wiki/Damselfly) are Damselflies. The variables of interest are `BodyWeight` and `TotalLength`. Let's use the dragonflies data subset. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So subset the data accordingly and remove NAs:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"Data2Fit <- subset(MyData,Suborder == \"Anisoptera\")\n",
"\n",
"Data2Fit <- Data2Fit[!is.na(Data2Fit$TotalLength),] # remove NA's"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot it:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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Vp5o8BsFKBYigdnsUeYQCNWeWNkLBWK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\nFVMB7wAAAABJRU5ErkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(Data2Fit$TotalLength, Data2Fit$BodyWeight)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Or, using `ggplot`:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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s+V1zimp3nxGBbEEkTB7g3Z/FoWeEMX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\nsNIAAAAASUVORK5CYII=",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"library(\"ggplot2\")\n",
"\n",
"ggplot(Data2Fit, aes(x = TotalLength, y = BodyWeight)) + geom_point()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Remember, when you write this analysis into a stand-alone R script, you should put all commands for loading packages (`library()`, `require()`) at the start of the script.* \n",
"\n",
"Now fit the model to the data using NLLS:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"PowFit <- nlsLM(BodyWeight ~ powMod(TotalLength, a, b), data = Data2Fit, start = list(a = .1, b = .1))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Before proceeding further, have a look at what nlsLM's arguments are:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"?nlsLM"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that NLLS fitting requires \"starting values\" for the parameters (two in this case: `a` and `b`). \n",
"\n",
"Having obtained the fit, we can use `summary()` just like we would for a `lm()` fit object. "
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Formula: BodyWeight ~ powMod(TotalLength, a, b)\n",
"\n",
"Parameters:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"a 3.941e-06 2.234e-06 1.764 0.083 . \n",
"b 2.585e+00 1.348e-01 19.174 <2e-16 ***\n",
"---\n",
"Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
"\n",
"Residual standard error: 0.02807 on 58 degrees of freedom\n",
"\n",
"Number of iterations to convergence: 39 \n",
"Achieved convergence tolerance: 1.49e-08\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"summary(PowFit)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Most of the output is analogous to the output of an `lm()`. However, further statistical inference here cannot be done using Analysis of Variance (ANOVA), because the model is not a Linear Model. Try `anova(PowFit)`, and see what happens. The `Number of iterations to convergence`, and `Achieved convergence tolerance` stem from the fact that NLLS fitting requires computer simulations; revisit the [Lecture](https://github.com/mhasoba/TheMulQuaBio/blob/master/lectures/NLLS) for an explanation of this."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's visualize the fit. For this, first we need to generate a vector of body lengths (the x-axis variable) for plotting: "
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"Lengths <- seq(min(Data2Fit$TotalLength),max(Data2Fit$TotalLength),len=200)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, calculate the predicted line. For this, we will need to extract the coefficient from the model fit object using the `coef()`command. "
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<strong>a:</strong> 3.94068491030517e-06"
],
"text/latex": [
"\\textbf{a:} 3.94068491030517e-06"
],
"text/markdown": [
"**a:** 3.94068491030517e-06"
],
"text/plain": [
" a \n",
"3.940685e-06 "
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"<strong>b:</strong> 2.58504796772587"
],
"text/latex": [
"\\textbf{b:} 2.58504796772587"
],
"text/markdown": [
"**b:** 2.58504796772587"
],
"text/plain": [
" b \n",
"2.585048 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"coef(PowFit)[\"a\"]\n",
"coef(PowFit)[\"b\"]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So, we can do the following:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"Predic2PlotPow <- powMod(Lengths,coef(PowFit)[\"a\"],coef(PowFit)[\"b\"])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now plot the data and the fitted model line:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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82bNxcuXAgODlZTU6tpJJFI69at09fX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klAglMa4jR44AwJ9//tlUBUkMysXFRUVF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\nqYaJECGEkFT7f5CQcyGdtjj2AAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(Data2Fit$TotalLength, Data2Fit$BodyWeight)\n",
"lines(Lengths, Predic2PlotPow, col = 'blue', lwd = 2.5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can claculate the confidence intervals on the estimated parameters as we would in OLS fitting used for Linear Models: "
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Waiting for profiling to be done...\n"
]
},
{
"data": {
"text/html": [
"<table>\n",
"<thead><tr><th></th><th scope=col>2.5%</th><th scope=col>97.5%</th></tr></thead>\n",
"<tbody>\n",
"\t<tr><th scope=row>a</th><td>1.171935e-06</td><td>1.205273e-05</td></tr>\n",
"\t<tr><th scope=row>b</th><td>2.318292e+00</td><td>2.872287e+00</td></tr>\n",
"</tbody>\n",
"</table>\n"
],
"text/latex": [
"\\begin{tabular}{r|ll}\n",
" & 2.5\\% & 97.5\\%\\\\\n",
"\\hline\n",
"\ta & 1.171935e-06 & 1.205273e-05\\\\\n",
"\tb & 2.318292e+00 & 2.872287e+00\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| <!--/--> | 2.5% | 97.5% | \n",
"|---|---|\n",
"| a | 1.171935e-06 | 1.205273e-05 | \n",
"| b | 2.318292e+00 | 2.872287e+00 | \n",
"\n",
"\n"
],
"text/plain": [
" 2.5% 97.5% \n",
"a 1.171935e-06 1.205273e-05\n",
"b 2.318292e+00 2.872287e+00"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"confint(PowFit)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you likely have learnt before, a coefficient's CI should not include zero for it to be statistically significant (different from zero). "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercises <a id='Allom_Exercises'></a>\n",
"\n",
"(a) Make the same plot as above, fitted line and all, in `ggplot`, and add (display) the equation you estimated to your new (ggplot) plot. The equation is: $\\text{Weight} = 3.94 \\times 10^{-06} \\times \\text{Length}^{2.59}$\n",
"\n",
"(b) Try playing with the starting values, and see if you can \"break\" the model fitting -- that is, change the starting values till the NLLS fitting does not converge on a solution.\n",
"\n",
"(c) Repeat the model fitting (including a-b above) using the Zygoptera data subset.\n",
"\n",
" \n",
"(d) There is an alternative (and in fact, more commonly-used) approach for fitting the allometric model to data: using Ordinary Least Squares on bi-logarithamically transformed data. That is, if you take a log of both sides of the [allometric equation](#eq:allom) we get,\n",
"\n",
"$$\n",
"\\log(y) = \\log(a) + b \\log(x)\n",
"$$\n",
"\n",
"This is a straight line equation of the form $c = d + b z $, where $c = \\log(c)$, $d = \\log(a)$, $z = \\log(x)$, and $b$ is now the slope parameter. So you can use Ordinary Least Squares and the linear models framework (with `lm()`) in R to estimate the parameters of the allometric equation. \n",
"\n",
"In this exercise, try comparing the NLLS vs OLS methods to see how much difference you get in the parameter estimates between them. For example, see the methods used in this paper by [Cohen et al 2012](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3465447/).\n",
"\n",
"(e) The allometry between Body weight and Length is not the end of the story. You have a number of other linear morphological measurements (`HeadLength`, `ThoraxLength`, `AdbdomenLength`, `ForewingLength`, `HindwingLength`, `ForewingArea`, and `HindwingArea`) that can also be investigated. In this exercise, try two lines of investigation (again, repeated separately for Dragonflies and Damselfiles): \n",
"\n",
" (i) How do each of these measures allometrically scale with Body length (obtain estimates of scaling constant and exponent)? (Hint: you may want to use the `pairs()` command in R to get an overview of all the pairs of potential scaling relationships. \n",
"\n",
" (ii) Do any of the linear morphological measurements other than body length better predict Body weight? That is, does body weight scale more tightly with a linear morphological measurement other than total body length? You would use model selection here, which we will learn next. But for now, you can just look at and compare the $R^2$ values of the models."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Comparing models\n",
"\n",
"*How do we know that there isn't a better or alternative model that adequately explains the pattern in your dataset?* \n",
"\n",
"This is important consideration in all data analyses (and more generally, the scientific method!), so you must aim to compare your NLLS model with an one or more alternatives for a more extensive and reliable investigation of the problem. \n",
"\n",
"Let's use model comparison to investigate whether the relationship between body weight and length we found above is indeed allometric. For this, we need an alternative model that can be fitted to the same data. Let's try a quadratic curve, which is of the form:\n",
"\n",
"$$\n",
"y = a + b x + c x^2\n",
"$$\n",
"\n",
"This can also capture curvature in data, and is an alternative model to the [allometric equation](#eq:allom). Note that this mode is linear in its parameters (a linear model), which you can fit to the simply data using your familiar `lm()` function: "
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"QuaFit <- lm(BodyWeight ~ poly(TotalLength,2), data = Data2Fit)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And like before, we obtain the predicted values (but this time using the `predict.lm` function):"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [],
"source": [
"Predic2PlotQua <- predict.lm(QuaFit, data.frame(TotalLength = Lengths))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's plot the two fitted models together:"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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M6H89LpdITQ8+fP+XCuH9X+FeGjR4/s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\nT0tLy+Li4qCgoCVLlujo6Li4uPAwqBFCCElISCQmJv7999+3b99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RvfUXNNdvvW7khB7gaxkksbo126QL0ghjutdbyEOGDHn16pWBgcGe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AUFRUJCMjI7aLpGIiRAghJNa6VacZQggh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\neDB1UV9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"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(Data2Fit$TotalLength, Data2Fit$BodyWeight)\n",
"lines(Lengths, Predic2PlotPow, col = 'blue', lwd = 2.5)\n",
"lines(Lengths, Predic2PlotQua, col = 'red', lwd = 2.5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Very similar fits, except that the quadratic model seems to deviate a bit from the data at the lower end of the data range. Let's do a proper, formal model comparison now to check which model better-fits the data.\n",
"\n",
"First calculate the R$^2$ values of the two fitted models:"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"0.90054752976309"
],
"text/latex": [
"0.90054752976309"
],
"text/markdown": [
"0.90054752976309"
],
"text/plain": [
"[1] 0.9005475"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"0.900302864503218"
],
"text/latex": [
"0.900302864503218"
],
"text/markdown": [
"0.900302864503218"
],
"text/plain": [
"[1] 0.9003029"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"RSS_Pow <- sum(residuals(PowFit)^2) # Residual sum of squares\n",
"TSS_Pow <- sum((Data2Fit$BodyWeight - mean(Data2Fit$BodyWeight))^2) # Total sum of squares\n",
"RSq_Pow <- 1 - (RSS_Pow/TSS_Pow) # R-squared value\n",
"\n",
"RSS_Qua <- sum(residuals(QuaFit)^2) # Residual sum of squares\n",
"TSS_Qua <- sum((Data2Fit$BodyWeight - mean(Data2Fit$BodyWeight))^2) # Total sum of squares\n",
"RSq_Qua <- 1 - (RSS_Qua/TSS_Qua) # R-squared value\n",
"\n",
"RSq_Pow \n",
"RSq_Qua"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Not very useful. In general, R$^2$ is a good measure of model fit, but cannot be used for model selection -- epecially not here, given the tiny difference in R$^2$'s.\n",
"\n",
"Instead, as explained in the [lecture](https://github.com/vectorbite/VBiTraining2/blob/master/lectures/ModelFitting), we can use the Akaike Information Criterion (AIC):"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"-2.1474260812509"
],
"text/latex": [
"-2.1474260812509"
],
"text/markdown": [
"-2.1474260812509"
],
"text/plain": [
"[1] -2.147426"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n <- nrow(Data2Fit) #set sample size\n",
"kPow <- length(coef(PowFit)) # get number of parameters in power law model\n",
"kQua <- length(coef(QuaFit)) # get number of parameters in quadratic model\n",
"\n",
"AIC_Pow <- n * log((2 * pi) / n) + n + 2 + n * log(RSS_Pow) + 2 * kPow\n",
"AIC_Qua <- n * log((2 * pi) / n) + n + 2 + n * log(RSS_Qua) + 2 * kQua\n",
"AIC_Pow - AIC_Qua"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Of course, as you might have suspected, we can do this using an in-built function in R! "
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"-2.1474260812509"
],
"text/latex": [
"-2.1474260812509"
],
"text/markdown": [
"-2.1474260812509"
],
"text/plain": [
"[1] -2.147426"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"AIC(PowFit) - AIC(QuaFit)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*So which model wins?* As we had dicussed in the NLLS lecture, a rule of thumb is that a AIC value difference (typically denoted as $\\Delta$AIC) > 2 is a acceptable cutoff for calling a winner. So the power law (allometric model) is a better fit here. Read the [Johnson & Omland paper](https://github.com/mhasoba/TheMulQuaBio/blob/master/readings/Modelling/JohnsonOmland2004.pdf) for more on model selection in Ecology and Evolution. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercises <a id='ModelSelection_Exercises'></a>\n",
"\n",
"(a) Calculate the Bayesian Information Criterion (BIC), also know as the Schwarz Criterion (see your Lecture notes and the [Johnson & Omland paper](https://github.com/mhasoba/TheMulQuaBio/blob/master/readings/Modelling/JohnsonOmland2004.pdf), and use $\\Delta$BIC to select the better fitting model. \n",
"\n",
"(b) Fit a straight line to the same data and compare with the allometric and quadratic models.\n",
"\n",
"(c) Repeat the model comparison (incuding 1-2 above) using the Damselflies (Zygoptera) data subset -- does the allometric model still win?\n",
"\n",
"(d) Repeat exercise (e)(i) and (ii) from the [above set](#Allom_Exercises), but with model comparison (e.g., again using a quadratic as an alternative model) to establish that the relationships are indeed allometric.\n",
"\n",
"(d) Repeat exercise (e)(ii) from the [above set](#Allom_Exercises), but with model comparison to establish which linear measurement is the best predictor of Body weight."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Albatross chick growth\n",
"\n",
"Now let's look at a different trait example: the growth of an individual albatross chick (you can find similar data for vector and non-vector arthropods in [VecTraits](http://vectorbyte.org/)). First load and plot the data:"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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ILzGjZSM24hHByQt17eBOAjVkxuBMyV0YtVt0UmHuLz/m/pIRzrvAjjY7I7eL07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",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"alb<-read.csv(file=\"../data/albatross_grow.csv\")\n",
"alb<-subset(x=alb, !is.na(alb$wt))\n",
"plot(alb$age, alb$wt, xlab=\"age (days)\", ylab=\"weight (g)\", xlim=c(0, 100))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Fitting the three models using NLLS\n",
"\n",
"Let's fit multiple mdoels to this dataset.\n",
"\n",
"The Von Bertalanffy model is commonly used for modelling the growth of an individual. It's formulation is:\n",
"\n",
"$$\n",
"W(t) = \\rho (L_{\\infty}(1-e^{-Kt})+L_0 e^{-Kt})^3\n",
"$$\n",
"\n",
"If we pull out $L_{\\infty}$ and define $c=L_0/L_{\\infty}$ and $W_{\\infty}=\\rho L_{\\infty}^3$ this equation becomes:\n",
"\n",
"$$\n",
"W(t) = W_{\\infty}(1-e^{-Kt}+ c e^{-Kt})^3.\n",
"$$\n",
"\n",
"$W_{\\infty}$ is interpreted as the mean asymptotic weight, and $c$ the ratio between the initial and final lengths. This second equation is the one we will fit.\n",
"\n",
"We will compare this model against the classical Logistic growth equation, and a straight line. First, as we did before, let's define the R functions for the two models:"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
"logistic1<-function(t, r, K, N0){\n",
" N0*K*exp(r*t)/(K+N0*(exp(r*t)-1))\n",
"}\n",
"\n",
"vonbert.w<-function(t, Winf, c, K){\n",
" Winf*(1 - exp(-K*t) + c*exp(-K*t))^3\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For the straight line, we use simply use R's `lm()` function, as that is a linear least squares problem. Using NLLS will give (approximately) the same answer, of course. Now fit all 3 models using least squares. \n",
"\n",
"We will scale the data before fitting to improve the stability of the estimates:"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [],
"source": [
"scale<-4000\n",
"\n",
"alb.lin<-lm(wt/scale~age, data=alb)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"alb.log<-nlsLM(wt/scale~logistic1(age, r, K, N0), start=list(K=1, r=0.1, N0=0.1), data=alb)\n",
"\n",
"alb.vb<-nlsLM(wt/scale~vonbert.w(age, Winf, c, K), start=list(Winf=0.75, c=0.01, K=0.01), data=alb)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next let's calculate predictions for each of the models across a range of ages."
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [],
"source": [
"ages<-seq(0, 100, length=1000)\n",
"\n",
"pred.lin<-predict(alb.lin, newdata = list(age=ages))*scale\n",
"\n",
"pred.log<-predict(alb.log, newdata = list(age=ages))*scale\n",
"\n",
"pred.vb<-predict(alb.vb, newdata = list(age=ages))*scale"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And finally plot the data with the fits:"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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2FGRsbSpUtdXV0fPnxobW3d5I1tBMHB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SSEjozZs3jo6Ozs7OJ0+epFKpzUtesWLF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\n/j82UcFossICnQAAAABJRU5ErkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(alb$age, alb$wt, xlab=\"age (days)\", ylab=\"weight (g)\", xlim=c(0,100))\n",
"lines(ages, pred.lin, col=2, lwd=2)\n",
"lines(ages, pred.log, col=3, lwd=2)\n",
"lines(ages, pred.vb, col=4, lwd=2)\n",
"\n",
"legend(\"topleft\", legend = c(\"linear\", \"logistic\", \"Von Bert\"), lwd=2, lty=1, col=2:4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next examine the residuals between the 3 models:"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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rACEYvACkQsAisQsQisQMQisAIRi8AKRCwCKxCxCKxAxCKwAhGLwApELAIrELEI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\nCAsShAUJwoIEYUGCsCBBWJB4AhSBuZWXm3wpAAAAAElFTkSuQmCC",
"text/plain": [
"Plot with title “VB resids”"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"par(mfrow=c(3,1), bty=\"n\")\n",
"plot(alb$age, resid(alb.lin), main=\"LM resids\", xlim=c(0,100))\n",
"plot(alb$age, resid(alb.log), main=\"Logisitic resids\", xlim=c(0,100))\n",
"plot(alb$age, resid(alb.vb), main=\"VB resids\", xlim=c(0,100))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The residuals for all 3 models still exhibit some patterns. In particular, the data seems to go down near the end of the observation period, but none of these models can capture that behavior. \n",
"\n",
"Finally, let's compare the 3 models using a simpler approach than the AIC/BIC one that we used [above](#Allom_Exercises) by calculating adjusted Sums of Squared Errors (SSE's):"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/html": [
"<dl>\n",
"\t<dt>$lin</dt>\n",
"\t\t<dd>0.00958</dd>\n",
"\t<dt>$log</dt>\n",
"\t\t<dd>0.0056</dd>\n",
"\t<dt>$vb</dt>\n",
"\t\t<dd>0.00628</dd>\n",
"</dl>\n"
],
"text/latex": [
"\\begin{description}\n",
"\\item[\\$lin] 0.00958\n",
"\\item[\\$log] 0.0056\n",
"\\item[\\$vb] 0.00628\n",
"\\end{description}\n"
],
"text/markdown": [
"$lin\n",
": 0.00958\n",
"$log\n",
": 0.0056\n",
"$vb\n",
": 0.00628\n",
"\n",
"\n"
],
"text/plain": [
"$lin\n",
"[1] 0.00958\n",
"\n",
"$log\n",
"[1] 0.0056\n",
"\n",
"$vb\n",
"[1] 0.00628\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n<-length(alb$wt)\n",
"list(lin=signif(sum(resid(alb.lin)^2)/(n-2*2), 3), \n",
" log= signif(sum(resid(alb.log)^2)/(n-2*3), 3), \n",
" vb= signif(sum(resid(alb.vb)^2)/(n-2*3), 3)) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The logistic model has the lowest adjusted SSE, so it's the best by this measure. It is also, visually, a better fit. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercises <a id='Albatross_Exercises'></a>\n",
"\n",
"(a) Use AIC/BIC to perform model selection on the Albatross data as we did for the trait allometry example.\n",
"\n",
"(b) Write this example as a self-sufficient R script, with ggplot istead of base plotting "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Aedes aegypti fecundity\n",
"\n",
"Now let's actually look at a disease vector example! These data measure the reponse of *Aedes aegypti* fecundity to temperature. \n",
"\n",
"First load and visualize the data:"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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UAsh0AsLUAsh0AsLUAsh0AsLUAsh0AsLRgmVoLaLWJaGK+S2VkTC5sxNbzNjylV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",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"aedes<-read.csv(file=\"../data/aedes_fecund.csv\")\n",
"\n",
"plot(aedes$T, aedes$EFD, xlab=\"temperature (C)\", ylab=\"Eggs/day\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The TPC models\n",
"\n",
"Let's define some models first:"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [],
"source": [
"quad1 <- function(T, T0, Tm, c){\n",
" c*(T-T0)*(T-Tm)*as.numeric(T<Tm)*as.numeric(T>T0)\n",
"}\n",
"\n",
"briere <- function(T, T0, Tm, c){\n",
" c*T*(T-T0)*(abs(Tm-T)^(1/2))*as.numeric(T<Tm)*as.numeric(T>T0)\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Instead of using the inbuilt quadratic function in R, we we define our own to make it easier to choose starting values, and so that we can force the function to be equal to zero above and below the minimum and maximum temperature thresholds (more on this below). The Briere function is a commonly used model for tempoeratuire dependence of insect traits. As in the case of the albatross growth data, we will also compare these two with a strauight line (again, its a linear model, so we can just use `lm()` without needing to define a function for it). \n",
"\n",
"Now fit all 3 models using least squares. Although it's not as necessary here (as the data don't have as large values as the albatross example), we will again scale the data first: "
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [],
"source": [
"scale <- 20\n",
"\n",
"aed.lin <- lm(EFD/scale~T, data=aedes)\n",
"\n",
"aed.quad <- nlsLM(EFD/scale~quad1(T, T0, Tm, c), start=list(T0=10, Tm=40, c=0.01), data=aedes)\n",
"\n",
"aed.br <- nlsLM(EFD/scale~briere(T, T0, Tm, c), start=list(T0=10, Tm=40, c=0.1), data=aedes)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercises <a id='Aedes_Exercises'></a>\n",
"\n",
"(a) Complete the *Aedes* data analysis by fitiing model, calculating predictions and then comparing models. Write a single, self-standing script for it. Which model fits best? By what measure?\n",
"\n",
"(b) In this script, use ggplot instead of base plotting."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Abundances as an example\n",
"\n",
"### Why Abundances?\n",
"\n",
"Fluctuations in the abundance (density) of a disease's vector play a crucial role in its transmission dynamics. This is especially true if vector population densities or their traits change at the same or shorter timescales than the rate of disease transmission. Indeed, most vectors are small ectotherms with short generation times and greater sensitivity to environmental conditions than their (invariably larger, longer-lived, and often, endothermic) hosts. So understanding how vector populations vary over time, space, and with respect to environmental variables such as temperature and preciptation is key. We will look at fitting models to the growth of a single population here. Time series analyses are coever in a separate [session](./TimeSeries.ipynb).\n",
"\n",
"### Population growth rate example\n",
"\n",
"A population grows exponentially while its abundance is low and resources are not limiting (the Malthusian principle). This growth then slows and eventually stops as resources become limiting. There may also be a time lag before the population growth really takes off at the start. We will focus on microbial (specifically, bacterial) growth rates. Bacterial growth in batch culture follows a distinct set of phases; lag phase, exponential phase and stationary phase. During the lag phase a suite of transcriptional machinery is activated, including genes involved in nutrient uptake and metabolic changes, as bacteria prepare for growth. During the exponential growth phase, bacteria divide at a constant rate, the population doubling with each generation. When the carrying capacity of the media is reached, growth slows and the number of cells in the culture stabilises, beginning the stationary phase.\n",
"\n",
"Traditionally, microbial growth rates were measured by plotting cell numbers or culture density against time on a semi-log graph and fitting a straight line through the exponential growth phase – the slope of the line gives the maximum growth rate ($r_{max}$). Models have since been developed which we can use to describe the whole sigmoidal bacterial growth curve. \n",
"\n",
"Let's first generate some \"data\" on the number of bacterial cells as a function of time that we can play with:"
]
},
{
"cell_type": "code",
"execution_count": 104,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<table>\n",
"<thead><tr><th scope=col>t</th><th scope=col>LogN</th></tr></thead>\n",
"<tbody>\n",
"\t<tr><td> 0 </td><td>3.499293</td></tr>\n",
"\t<tr><td> 2 </td><td>3.647743</td></tr>\n",
"\t<tr><td> 4 </td><td>3.738444</td></tr>\n",
"\t<tr><td> 6 </td><td>3.905430</td></tr>\n",
"\t<tr><td> 8 </td><td>5.272912</td></tr>\n",
"\t<tr><td>10 </td><td>6.320606</td></tr>\n",
"</tbody>\n",
"</table>\n"
],
"text/latex": [
"\\begin{tabular}{r|ll}\n",
" t & LogN\\\\\n",
"\\hline\n",
"\t 0 & 3.499293\\\\\n",
"\t 2 & 3.647743\\\\\n",
"\t 4 & 3.738444\\\\\n",
"\t 6 & 3.905430\\\\\n",
"\t 8 & 5.272912\\\\\n",
"\t 10 & 6.320606\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"t | LogN | \n",
"|---|---|---|---|---|---|\n",
"| 0 | 3.499293 | \n",
"| 2 | 3.647743 | \n",
"| 4 | 3.738444 | \n",
"| 6 | 3.905430 | \n",
"| 8 | 5.272912 | \n",
"| 10 | 6.320606 | \n",
"\n",
"\n"
],
"text/plain": [
" t LogN \n",
"1 0 3.499293\n",
"2 2 3.647743\n",
"3 4 3.738444\n",
"4 6 3.905430\n",
"5 8 5.272912\n",
"6 10 6.320606"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"time <- c(0, 2, 4, 6, 8, 10, 12, 16, 20, 24) # timepoints, in hours\n",
"log_cells <- c(3.62, 3.62, 3.63, 4.14, 5.23, 6.27, 7.57, 8.38, 8.70, 8.69) # logged cell counts - more on this below\n",
"\n",
"set.seed(1234) # set seed to ensure you always get the same random sequence if fluctuations \n",
"\n",
"data <- data.frame(time, log_cells + rnorm(length(time),sd=.1)) # add some random error\n",
"\n",
"names(data) <- c(\"t\", \"LogN\")\n",
"\n",
"head(data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have added a vector of normally distributed errors to emulate random \"sampling errors\". Note also that the assumption of normality of errors underlies the statistical analyses of Ordinary NLLS fits, just as it underlies Ordinary Least Squares (your standard linear modelling). In this case, we are talking about log-normality because we are using logged cell counts. Why log them? Because NLLS often converges better if you linearize the data (and correspindingly, the model - see how the models are specified below). "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot the data:"
]
},
{
"cell_type": "code",
"execution_count": 105,
"metadata": {},
"outputs": [
{
"data": {},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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54AyxKw5AmwLAFLngDLErDkCbAsAUue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",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ggplot(data, aes(x = t, y = LogN)) + geom_point()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will fit three growth models, all of which are known to fit such population growth data, especially in microbes. These are a modified Gompertz model (Zwietering et. al., 1990), the Baranyi model (Baranyi, 1993) and the Buchanan model (or three-phase logistic model; Buchanan, 1997). Given a set of cell numbers (N) and times (t), each growth model can be described in terms of:\n",
"\n",
"$N_0$: Initial cell culture (Population) density (number of cells per unit volume) \n",
"\n",
"$N_{max}$: Maximum culture density (aka \"carrying capacity\") \n",
"\n",
"$r_{max}$: Maximum growth rate \n",
"\n",
"$t_{lag}$: Duration of the lag phase before the population starts growing exponentially\n",
" \n",
"First let's specify the model functions:"
]
},
{
"cell_type": "code",
"execution_count": 106,
"metadata": {},
"outputs": [],
"source": [
"baranyi_model <- function(t, r_max, N_max, N_0, t_lag){ # Baranyi model (Baranyi 1993)\n",
"return(N_max + log10((-1+exp(r_max*t_lag) + exp(r_max*t))/(exp(r_max*t) - 1 + exp(r_max*t_lag) * 10^(N_max-N_0))))\n",
"}\n",
"\n",
"buchanan_model <- function(t, r_max, N_max, N_0, t_lag){ # Buchanan model - three phase logistic (Buchanan 1997)\n",
" return(N_0 + (t >= t_lag) * (t <= (t_lag + (N_max - N_0) * log(10)/r_max)) * r_max * (t - t_lag)/log(10) +\n",
" (t >= t_lag) * (t > (t_lag + (N_max - N_0) * log(10)/r_max)) * (N_max - N_0))\n",
"}\n",
"\n",
"gompertz_model <- function(t, r_max, N_max, N_0, t_lag){ # Modified gompertz growth model (Zwietering 1990)\n",
" return(N_0 + (N_max - N_0) * exp(-exp(r_max * exp(1) * (t_lag - t)/((N_max - N_0) * log(10)) + 1)))\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is important to note that we have written the functions in log (to the base 10 - can also be base 2 or natural log) scale because we want to do the fitting in log scale (both model and data linearized). The interpretation of each of the the estimated/fitted paramters does not change if we take a log of the model's equation. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's generate some starting values for the NLLS fitting. We did not pay much attention to what starting values we used in the above example on fitting an allometric model because the power-law model is easy to fit using NLLS, and starting far from the optimal parameters does not matter too much. Here, we derive the starting values by using the actual data: "
]
},
{
"cell_type": "code",
"execution_count": 96,
"metadata": {},
"outputs": [],
"source": [
"N_0_start <- min(data$LogN)\n",
"N_max_start <- max(data$LogN)\n",
"t_lag_start <- data$t[which.max(diff(diff(data$LogN)))]\n",
"r_max_start <- max(diff(data$LogN))/mean(diff(data$t))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now fit the models:"
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {
"scrolled": false
},
"outputs": [],
"source": [
"fit_baranyi <- nlsLM(LogN ~ baranyi_model(t = t, r_max, N_max, N_0, t_lag), data,\n",
" list(t_lag=t_lag_start, r_max=r_max_start, N_0 = N_0_start, N_max = N_max_start))\n",
"\n",
"fit_buchanan <- nlsLM(LogN ~ buchanan_model(t = t, r_max, N_max, N_0, t_lag), data,\n",
" list(t_lag=t_lag_start, r_max=r_max_start, N_0 = N_0_start, N_max = N_max_start))\n",
"\n",
"fit_gompertz <- nlsLM(LogN ~ gompertz_model(t = t, r_max, N_max, N_0, t_lag), data,\n",
" list(t_lag=t_lag_start, r_max=r_max_start, N_0 = N_0_start, N_max = N_max_start))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You might get a warning that one or more of the models generated some NaNs during the fitting procedure for the given data. You can ignore the warning in this case. But not always – sometimes these NaNs mean that the equation is wrongly written, or that it generates NaNs across the whole range of the x-values, in which case the model is inappropriate for these data. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Get the model summaries:"
]
},
{
"cell_type": "code",
"execution_count": 107,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Formula: LogN ~ baranyi_model(t = t, r_max, N_max, N_0, t_lag)\n",
"\n",
"Parameters:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"t_lag 5.52751 0.34869 15.85 4.00e-06 ***\n",
"r_max 1.41823 0.09356 15.16 5.20e-06 ***\n",
"N_0 3.59209 0.08646 41.55 1.30e-08 ***\n",
"N_max 8.52886 0.08352 102.12 5.94e-11 ***\n",
"---\n",
"Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
"\n",
"Residual standard error: 0.143 on 6 degrees of freedom\n",
"\n",
"Number of iterations to convergence: 10 \n",
"Achieved convergence tolerance: 1.49e-08\n"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"\n",
"Formula: LogN ~ buchanan_model(t = t, r_max, N_max, N_0, t_lag)\n",
"\n",
"Parameters:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"t_lag 5.42029 0.24932 21.74 6.19e-07 ***\n",
"r_max 1.36647 0.06886 19.84 1.06e-06 ***\n",
"N_0 3.62849 0.07721 46.99 6.22e-09 ***\n",
"N_max 8.52330 0.07721 110.39 3.73e-11 ***\n",
"---\n",
"Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
"\n",
"Residual standard error: 0.1337 on 6 degrees of freedom\n",
"\n",
"Number of iterations to convergence: 9 \n",
"Achieved convergence tolerance: 1.49e-08\n"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"\n",
"Formula: LogN ~ gompertz_model(t = t, r_max, N_max, N_0, t_lag)\n",
"\n",
"Parameters:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"t_lag 5.76455 0.26923 21.41 6.77e-07 ***\n",
"r_max 1.57526 0.09930 15.86 3.98e-06 ***\n",
"N_0 3.60201 0.07068 50.96 3.83e-09 ***\n",
"N_max 8.65943 0.08526 101.56 6.14e-11 ***\n",
"---\n",
"Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
"\n",
"Residual standard error: 0.1191 on 6 degrees of freedom\n",
"\n",
"Number of iterations to convergence: 8 \n",
"Achieved convergence tolerance: 1.49e-08\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"summary(fit_baranyi)\n",
"summary(fit_buchanan)\n",
"summary(fit_gompertz)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And see how the fits look:"
]
},
{
"cell_type": "code",
"execution_count": 108,
"metadata": {},
"outputs": [
{
"data": {},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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ydSi8PFspUsHtBc7tl4EEINCCZC5AvSrhCsoBHLV7WbRjbu4dl4EEINCCZC1OAJ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"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"timepoints <- seq(0, 24, 0.1)\n",
"\n",
"baranyi_points <- baranyi_model(t = timepoints, r_max = coef(fit_baranyi)[\"r_max\"], N_max = coef(fit_baranyi)[\"N_max\"], N_0 = coef(fit_baranyi)[\"N_0\"], t_lag = coef(fit_baranyi)[\"t_lag\"])\n",
"\n",
"buchanan_points <- buchanan_model(t = timepoints, r_max = coef(fit_buchanan)[\"r_max\"], N_max = coef(fit_buchanan)[\"N_max\"], N_0 = coef(fit_buchanan)[\"N_0\"], t_lag = coef(fit_buchanan)[\"t_lag\"])\n",
"\n",
"gompertz_points <- gompertz_model(t = timepoints, r_max = coef(fit_gompertz)[\"r_max\"], N_max = coef(fit_gompertz)[\"N_max\"], N_0 = coef(fit_gompertz)[\"N_0\"], t_lag = coef(fit_gompertz)[\"t_lag\"])\n",
"\n",
"df1 <- data.frame(timepoints, baranyi_points)\n",
"df1$model <- \"Baranyi\"\n",
"names(df1) <- c(\"t\", \"LogN\", \"model\")\n",
"\n",
"df2 <- data.frame(timepoints, buchanan_points)\n",
"df2$model <- \"Buchanan\"\n",
"names(df2) <- c(\"t\", \"LogN\", \"model\")\n",
"\n",
"df3 <- data.frame(timepoints, gompertz_points)\n",
"df3$model <- \"Gompertz\"\n",
"names(df3) <- c(\"t\", \"LogN\", \"model\")\n",
"\n",
"model_frame <- rbind(df1, df2, df3)\n",
"\n",
"ggplot(data, aes(x = t, y = LogN)) +\n",
" geom_point(size = 3) +\n",
" geom_line(data = model_frame, aes(x = t, y = LogN, col = model), size = 1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercises\n",
"\n",
"(a) Calculate the confidence intervals on the parameters of each of the three fitted models, and use model selection (using AIC and/or BIC) as you did before to see if you can determine the best-fitting model among the three.\n",
"\n",
"(b) Alternatively, for a different random sequence of fluctuations, one or more of the models may fail to fit (a `singular gradiant matrix` error). Try repeating the above fitting with a different random seed (change the integers given to the `random.seed( )` function), or increase the sampling error by increasing the standard deviationand see if it happens. If/when the NLLS optimization does fail to converge (the RSS minimum was not found), you can try to fix it by chaning the starting values. \n",
"\n",
"(c) Repeat the model comparison exercise 1000 times (You will have to write a loop), and determine if/whether one model generally wins more often than the others. Note that each run will generate a slightly different dataset, because we are adding a vector of random errors every time the \"data\" are generated. This may result in failure of the NLLS fitting to converge, in which case you will need to use the [`try()` or `tryCatch` functions](https://nbviewer.jupyter.org/github/mhasoba/TheMulQuaBio/blob/master/notebooks/07-R.ipynb).\n",
"\n",
"(d) Repeat (b), but increase the error by increasing the standard deviation of the normal error distributon, and see if there are differences in the robustness of the models to sampling/experimental errors. You may also want to try changing the distribution of the errors to some non-normal distribution and see what happens."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model fitting using Maximum Likelihood\n",
"\n",
"Above we learned how to fit a mathematical model/equation to data by using the Least Squares method (linear or nonlinear). That is, we choose the parameters of model being fitted (e.g., straight line) to minimize the sum of the squares of the residuals/errors sround the fitted model. An alternative to minimizing the sum of squared errors is to find parameters to the function such that the *likelihood* of the parameters, given the data and the model, is maximized. Please see the [lectures](https://github.com/vectorbite/VBiTraining2/tree/master/lectures) for the theoretical background to the following R examples.\n",
"\n",
"We will first implement the (negative log) likelihood for simple linear regression (SLR) in R. Recall that SLR assumes every observation in the dataset was generated by the model:\n",
"\n",
"$$Y_i = \\beta_0 + \\beta_1 X_i + \\varepsilon_i, \\;\\;\\; \\varepsilon_i \\stackrel{\\mathrm{iid}}{\\sim} \\mathrm{N}(0, \\sigma^2)\n",
"$$\n",
"\n",
"That is, this is a model for the *conditional distribution* of $Y$ given $X$. The pdf for the normal distribution is given by\n",
"\n",
"$$\n",
"f(x) = \\frac{1}{\\sqrt{2\\sigma^2 \\pi}} \\exp\\left(-\\frac{(x-\\mu)^2}{2\\sigma^2} \\right)\n",
"$$\n",
"\n",
"In the SLR model, the conditional distribution has *this* distribution. \n",
"\n",
"That is, for any single observation, $y_i$\n",
"$$\n",
"f(y_i|\\beta_0, \\beta_1, x_i) = \\frac{1}{\\sqrt{2\\sigma^2 \\pi}} \\exp\\left(-\\frac{(y_i-(\\beta_0+\\beta_1 x_i))^2}{2\\sigma^2} \\right)\n",
"$$\n",
"\n",
"Interpreting this function as a function of the parameters $\\theta=\\{ \\beta_0, \\beta_1, \\sigma \\}$, then it gives us the likelihood of the $i^{\\mathrm{th}}$ data point. \n",
"\n",
"As we did for the simple binomial distribution (see [lecture](https://github.com/vectorbite/VBiTraining2/tree/master/lectures)), we can use this to estimate the parameters of the model."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Implementing the Likelihood in R\n",
"\n",
"First, we need to build an R function that returns the (negative log) likelihood for simple linear regression (it is negative log because the log of likelihood is itself negative):"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {},
"outputs": [],
"source": [
"nll.slr <- function(par, dat, ...){\n",
" args <- list(...)\n",
" \n",
" b0 <- par[1]\n",
" b1 <- par[2]\n",
" X <- dat$X\n",
" Y <- dat$Y\n",
" if(!is.na(args$sigma)){\n",
" sigma <- args$sigma\n",
" } else \n",
" sigma <- par[3]\n",
"\n",
" mu <- b0+b1*X\n",
" \n",
" return(-sum(dnorm(Y, mean=mu, sd=sigma, log=TRUE)))\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that we do something a bit different here (the \"`...`\" bit). We do it this way because we want to be able to use R's `optim()` function later.\n",
"\n",
"The `dnorm()` function calculates the logged (the `log=TRUE` argument) probability of observing Y given mu, sigma and that X. \n",
"\n",
"The negative sign on `sum()` is because the `optim()` function in R will minimize the negative log-likelihood, which is a sum: Recall that The log-likelihood of the parameters $\\theta$ being true given data x equals to the sum of the logged probability densities of observing the data x given parameters $\\theta$. We want to maximize this (log-) likelihood using `optim()`."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's generate some simulated data, assuming that: $\\beta_0=$ `b0`, $\\beta_1=$ `b1`, and $\\sigma=$ `sigma`. For this, we will generate random deviations to simulate sampling or measurement error around an otherwise perfect line of data values:"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {},
"outputs": [],
"source": [
"set.seed(123)\n",
"n <- 30\n",
"b0 <- 10\n",
"b1 <- 3\n",
"sigma <- 2\n",
"X <- rnorm(n, mean=3, sd=7)\n",
"Y <- b0 + b1*X + rnorm(n, mean=0, sd=sigma)\n",
"dat <- data.frame(X=X, Y=Y) # convert to a data frame"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the first line, we `set.seed()` to ensure that we can reproduce the results. The seed number you choose is the starting point used in the generation of a sequence of random numbers. No plot the \"data\":"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {},
"outputs": [
{
"data": {
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vikhEl2SpijaJ/l39JHggawBoIGVhA0sIKggRUEDawgaGAFQQMrCBpYQdDACoIG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\nRK5CYII=",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(X, Y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Likelihood profile in R\n",
"\n",
"For now, let's assume that we know what $\\beta_1$ is. Let's build a likelihood profile for the simulated data:"
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {},
"outputs": [],
"source": [
"N <- 50\n",
"b0s <- seq(5, 15, length=N)\n",
"mynll <- rep(NA, length=50)\n",
"for(i in 1:N){\n",
" mynll[i] <- nll.slr(par=c(b0s[i],b1), dat=dat, sigma=sigma)\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That is, we calculate the negative log-likelihood for fixed b1, across a range (5 - 15) of b0. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now plot the profile:"
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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sOMwVFZWamjoyMuLt7OMSIiInp6eoL2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\n",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(b0s, mynll, type=\"l\")\n",
"abline(v=b0, col=2)\n",
"abline(v=b0s[which.min(mynll)], col=3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The true value for b0 (10) is the red line, while the value that minimizes the log-likelihood (i.e., maximizes the negative log-likelihood) is the green line. These are not the same because maximum likelihood is providing an *estimate* of the true value given the measurement errors (that we ourselves generated in tgis synthetic dataset). "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Likelihood surface in R\n",
"\n",
"If we wanted to estimate both $\\beta_0$ and $\\beta_1$ (two parameters), we need to deal with a two-dimensional maximum likelihood surface. The simplest approach is to do a *grid search* to find this likelihood surface."
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/html": [
"<table>\n",
"<tbody>\n",
"\t<tr><td>10.00000</td><td>3.00 </td></tr>\n",
"\t<tr><td>10.48485</td><td>2.96 </td></tr>\n",
"</tbody>\n",
"</table>\n"
],
"text/latex": [
"\\begin{tabular}{ll}\n",
"\t 10.00000 & 3.00 \\\\\n",
"\t 10.48485 & 2.96 \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| 10.00000 | 3.00 | \n",
"| 10.48485 | 2.96 | \n",
"\n",
"\n"
],
"text/plain": [
" [,1] [,2]\n",
"[1,] 10.00000 3.00\n",
"[2,] 10.48485 2.96"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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QfLU23ggw/E4dA9CRERqa0VESktLW2Z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\nR3AAAADlCA4AAKAcwQEAAJT7/8uVPCkmUpw1AAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N0 <- 100\n",
"N1 <- 101\n",
"b0s <- seq(7,12, length=N0)\n",
"b1s <- seq(1,5, length=N1)\n",
"\n",
"mynll<-matrix(NA, nrow=N0, ncol=N1)\n",
"for(i in 1:N0){\n",
" for(j in 1:N1) mynll[i,j]<-nll.slr(par=c(b0s[i],b1s[j]), dat=dat, sigma=sigma)\n",
"}\n",
"\n",
"ww <- which(mynll==min(mynll), arr.ind=TRUE)\n",
"\n",
"b0.est <- b0s[ww[1]]\n",
"b1.est <- b1s[ww[2]]\n",
"rbind(c(b0, b1), c(b0.est, b1.est))\n",
"\n",
"filled.contour(x = b0s, y = b1s, z= mynll, col=heat.colors(21), \n",
" plot.axes = {axis(1); axis(2); points(b0,b1, pch=21); \n",
" points(b0.est, b1.est, pch=8, cex=1.5); xlab=\"b0\"; ylab=\"b1\"})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is a lot going on here. Make sure you ask one of us if some of the code does not make sense!\n",
"\n",
"Again, note that the true parameter combination (asterisk) and the one what maximizes the negative log-likelihood (circle) are different."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Conditional Likelihood\n",
"We can also look at the conditional surfaces (i.e., we look at the slice around whatever the best estimate is for the other parameter):"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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00xs2JMLPwSx++wR2j9CgttXPok10CcC8eh73yusPWM5DcFn/SistAPt+UaiMN5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\nbh3HqvAfzBfeU2aeuEhoYBXa/IGQsoU29tUawLxmdnHE2zxDcTb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"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"par(mfrow=c(1,2), bty=\"n\")\n",
"plot(b0s, mynll[,ww[2]], type=\"l\", xlab=\"b0\", ylab=\"NLL\")\n",
"plot(b1s, mynll[ww[1],], type=\"l\", xlab=\"b1\", ylab=\"NLL\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Alternatives to Grid Search\n",
"\n",
"There are many alternative methods to grid searches. Since we are seeking to minimize an arbitrary function (the negative log likelihood) we typically use a descent method to perform general optimization.\n",
"\n",
"There are lots of options implemented in the `optim`function in R. We won't go into the details of these methods, due to time constraints. However, typically one would most commonly use:\n",
"\n",
"* Brent's method: for 1-D search within a bounding box, only\n",
"* L-BFGS-B (limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm with bounding box constraints): a quasi-Newton method, used for higher dimensions, when you want to be able to put simple limits on your search area. \n",
" \n",
"\n",
"### Maximum Likelihood using `optim()`\n",
"\n",
"We can now do the fitting. This involves optimization (to find the appropriate parameter values that achieve the maximum of the likelihood surface above). For this, we will use R's versatile `optim()` function.\n",
"\n",
"The first argument for `optim()` is the function that you want to minimize, and the second is a vector of starting values for your parameters (as always, do a`?optim`). After the main arguments, you can add what you need to evaluate your function (e.g. `sigma` ). The addtional argument sigma can be \"fed\" to `nll.slr` because we use the `...` convention when defining it."
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/html": [
"<dl>\n",
"\t<dt>$par</dt>\n",
"\t\t<dd><ol class=list-inline>\n",
"\t<li>10.4589351280817</li>\n",
"\t<li>2.96170447551098</li>\n",
"</ol>\n",
"</dd>\n",
"\t<dt>$value</dt>\n",
"\t\t<dd>58.2247252772924</dd>\n",
"\t<dt>$counts</dt>\n",
"\t\t<dd><dl class=dl-horizontal>\n",
"\t<dt>function</dt>\n",
"\t\t<dd>12</dd>\n",
"\t<dt>gradient</dt>\n",
"\t\t<dd>12</dd>\n",
"</dl>\n",
"</dd>\n",
"\t<dt>$convergence</dt>\n",
"\t\t<dd>0</dd>\n",
"\t<dt>$message</dt>\n",
"\t\t<dd>'CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH'</dd>\n",
"</dl>\n"
],
"text/latex": [
"\\begin{description}\n",
"\\item[\\$par] \\begin{enumerate*}\n",
"\\item 10.4589351280817\n",
"\\item 2.96170447551098\n",
"\\end{enumerate*}\n",
"\n",
"\\item[\\$value] 58.2247252772924\n",
"\\item[\\$counts] \\begin{description*}\n",
"\\item[function] 12\n",
"\\item[gradient] 12\n",
"\\end{description*}\n",
"\n",
"\\item[\\$convergence] 0\n",
"\\item[\\$message] 'CONVERGENCE: REL\\_REDUCTION\\_OF\\_F <= FACTR*EPSMCH'\n",
"\\end{description}\n"
],
"text/markdown": [
"$par\n",
": 1. 10.4589351280817\n",
"2. 2.96170447551098\n",
"\n",
"\n",
"\n",
"$value\n",
": 58.2247252772924\n",
"$counts\n",
": function\n",
": 12gradient\n",
": 12\n",
"\n",
"\n",
"$convergence\n",
": 0\n",
"$message\n",
": 'CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH'\n",
"\n",
"\n"
],
"text/plain": [
"$par\n",
"[1] 10.458935 2.961704\n",
"\n",
"$value\n",
"[1] 58.22473\n",
"\n",
"$counts\n",
"function gradient \n",
" 12 12 \n",
"\n",
"$convergence\n",
"[1] 0\n",
"\n",
"$message\n",
"[1] \"CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH\"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fit <- optim(nll.slr, par=c(2, 1), method=\"L-BFGS-B\", ## this is a n-D method\n",
" lower=-Inf, upper=Inf, dat=dat, sigma=sigma)\n",
"\n",
"fit"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Easy as pie (once you have the recipe)! We can also fit sigma as the same time if we want:"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/html": [
"<ol class=list-inline>\n",
"\t<li>10.4589449542964</li>\n",
"\t<li>2.96170371229526</li>\n",
"\t<li>1.62168936031414</li>\n",
"</ol>\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 10.4589449542964\n",
"\\item 2.96170371229526\n",
"\\item 1.62168936031414\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 10.4589449542964\n",
"2. 2.96170371229526\n",
"3. 1.62168936031414\n",
"\n",
"\n"
],
"text/plain": [
"[1] 10.458945 2.961704 1.621689"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fit <- optim(nll.slr, par=c(2, 1, 5), method=\"L-BFGS-B\", ## this is a n-D method\n",
" lower=c(-Inf, -Inf, 0.1), upper=Inf, dat=dat, sigma=NA)\n",
"fit$par"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The starting values (b0 = 2, b1 = 1, sigma = 5) need to be assigned as we would do for NLLS. Also note that much like NLLS, we have bounded the parameters. The exact starting values are not too important in this case (try changing them see what happens)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now visualize the fit:"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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hptmI3NGbHYaPZsFBRAJIKvb/HZs2uu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\nR+EAAACGo3AAAADDUTgAAIDh/g9p29+S6WXKkQAAAABJRU5ErkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(X, Y)\n",
"abline(a=fit$par[1], b=fit$par[2], col=2, lwd=2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Confidence intervals\n",
"\n",
"The joint distribution of the MLEs are asymptotically Normally distributed. Given this, if you are minimizing the negative log likelihood (NLL) then the covariance matrix of the estimates is (asymptotically) the inverse of the Hessian matrix. The Hessian matrix evalutes the second derivatives of the NLL (numerically here), which gives us information about the curvature the likelihood. Thus we can use the Hessian to estimate confidence intervals:"
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/html": [
"<table>\n",
"<thead><tr><th scope=col>value</th><th scope=col>upper</th><th scope=col>lower</th></tr></thead>\n",
"<tbody>\n",
"\t<tr><td>10.458935</td><td>11.228565</td><td>9.689305 </td></tr>\n",
"\t<tr><td> 2.961704</td><td> 3.067705</td><td>2.855704 </td></tr>\n",
"</tbody>\n",
"</table>\n"
],
"text/latex": [
"\\begin{tabular}{r|lll}\n",
" value & upper & lower\\\\\n",
"\\hline\n",
"\t 10.458935 & 11.228565 & 9.689305 \\\\\n",
"\t 2.961704 & 3.067705 & 2.855704 \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"value | upper | lower | \n",
"|---|---|\n",
"| 10.458935 | 11.228565 | 9.689305 | \n",
"| 2.961704 | 3.067705 | 2.855704 | \n",
"\n",
"\n"
],
"text/plain": [
" value upper lower \n",
"1 10.458935 11.228565 9.689305\n",
"2 2.961704 3.067705 2.855704"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fit <- optim(nll.slr, par=c(2, 1), method=\"L-BFGS-B\", hessian=TRUE, lower=-Inf, upper=Inf, dat=dat, sigma=sigma)\n",
"\n",
"fisher_info<-solve(fit$hessian)\n",
"est_sigma<-sqrt(diag(fisher_info))\n",
"upper<-fit$par+1.96*est_sigma\n",
"lower<-fit$par-1.96*est_sigma\n",
"interval<-data.frame(value=fit$par, upper=upper, lower=lower)\n",
"interval"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Comparison to fitting with least squares\n",
"\n",
"We can, of course, simply fit the model with lest squares using the `lm()` function:"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/html": [
"<table>\n",
"<thead><tr><th></th><th scope=col>Estimate</th><th scope=col>Std. Error</th><th scope=col>t value</th><th scope=col>Pr(>|t|)</th></tr></thead>\n",
"<tbody>\n",
"\t<tr><th scope=row>(Intercept)</th><td>10.458936 </td><td>0.32957007 </td><td>31.73509 </td><td>1.699822e-23</td></tr>\n",
"\t<tr><th scope=row>X</th><td> 2.961704 </td><td>0.04539126 </td><td>65.24834 </td><td>3.874555e-32</td></tr>\n",
"</tbody>\n",
"</table>\n"
],
"text/latex": [
"\\begin{tabular}{r|llll}\n",
" & Estimate & Std. Error & t value & Pr(>\\textbar{}t\\textbar{})\\\\\n",
"\\hline\n",
"\t(Intercept) & 10.458936 & 0.32957007 & 31.73509 & 1.699822e-23\\\\\n",
"\tX & 2.961704 & 0.04539126 & 65.24834 & 3.874555e-32\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| <!--/--> | Estimate | Std. Error | t value | Pr(>|t|) | \n",
"|---|---|\n",
"| (Intercept) | 10.458936 | 0.32957007 | 31.73509 | 1.699822e-23 | \n",
"| X | 2.961704 | 0.04539126 | 65.24834 | 3.874555e-32 | \n",
"\n",
"\n"
],
"text/plain": [
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) 10.458936 0.32957007 31.73509 1.699822e-23\n",
"X 2.961704 0.04539126 65.24834 3.874555e-32"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lmfit<-lm(Y~X)\n",
"\n",
"summary(lmfit)$coeff"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The estimates we get using `optim()` are almost identical to the estimates that we obtain here, and the standard errors on the intercept and slope are very similar to those we calculated from the Hessian (est_sigma= `r est_sigma`). "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Model Selection\n",
"\n",
"You can use [AIC or BIC as you did in NLLS](#Comparing-models) using the likelihood you have calculated. \n",
"\n",
"You can also use the Likelihood Ratio Test (LRT).\n",
"\n",
"### Exercises <a id='MLE_Exercises'></a> \n",
"\n",
"Try MLE fitting for the allometric trait data example [above](#Allometric-scaling-of-traits). You will use the same data + functions that you used to practice fitting curves using non-linear least squares methods. You have two options here. The easier one is to convert the power law model to a straight line model by taking a log (explained the Allometry [Exercises](#Allom_Exercises). Specifically,\n",
"\n",
"(a) Using the [`nll.slr`](#Implementing-the-Likelihood-in-R) function as an example, write a function that calculates the negative log likelihood as a function of the parameters describing your trait and any additional parameters you need for an appropriate noise distribution (e.g., $\\sigma$ if you have normally distributed errors).\n",
"\n",
"(b) For at least one of your parameters plot a likelihood profile given your data, with the other parametes fixed.\n",
"\n",
"(c) Use the `optim` function to find the MLE of the same parameter and indicate this on your likelihood profile.\n",
"\n",
"(d) Obtain a confidence interval for your estimate.\n",
"\n",
"A more challenging option is to fit the allometry data directly to the power law equation. You would need to assume a log-normal distribution for the errors instead of normal, in this case. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Fitting Models the Bayesian way "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Recall from the [lectures](https://github.com/vectorbite/VBiTraining2/tree/master/lectures) that for Bayesian model fitting/inference, we need to: \n",
"\n",
"\n",
"1. **Assess MCMC convergence**: MCMC is family of algorithm for sampling probability distributions so that it can be adequately characterized (in the Bayesian context the posterior distribution). The MCMC procedure reaches *convergence* once we have sufficient random draws from the posterior distribution. To assess convergence we look at trace plots. The goal is to get \"fuzzy caterpillars\"-looking curves. \n",
"\n",
"2. **Summarize MCMC draws**: Summarize and visualize outcome of the random draws using histograms for all draws for each parameter, and calculate expectation, variance, credibility interval, etc.\n",
"\n",
"3. **Prior Sensitivity**: Assess prior sensitivity by changing prior values and check whether it affects the results or not. If it does, that means that the results are too sensitive to that prior, not good!\n",
"\n",
"4. **Make inferences**: We use the values from item (2) to make inferences and answer the research question.\n",
"\n",
"Because likelihoods form the basis for Bayesian model fitting, we will first do an exercise to understand their calculation. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### A Likelihoods exercise\n",
"\n",
"#### The Binomial Distribution\n",
"\n",
"The Binomial distribution is used to model the number of \"successes\" in a set of trials (e.g., number of heads when you flip a coin $N$ times). The pmf is \n",
"$$\n",
"{N \\choose x} p^x(1-p)^{N-x}\n",
"$$\n",
"such that $\\mathrm{E}[x]=Np$. Throughout this \"experiment\", you will assume that your experiment consists of flipping 20 coins, so that $N=20$.\n",
"\n",
"Let's use the Binomial distribution to practice two methods of estimating parameters for a probability distribution: method of moments and maximum likelihood.\n",
"\n",
"##### Simulating from the Binomial using R\n",
"\n",
"First take 50 draws from a binomial (using _rbinom_) for each $p\\in$ 0.1, 0.5, 0.8 with $N=20$. For this, lets set seed so that we can reproduce this exact sequence of sampling (why?):"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"set.seed(54321)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"## 50 draws with each p \n",
"pp<-c(0.1, 0.5, 0.8)\n",
"N<-20\n",
"reps<-50 "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now plot the histograms of these draws together with the density functions."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"## histograms + density here\n",
"x<-seq(0, 50, by=1)\n",
"par(mfrow=c(1,3), bty=\"n\")\n",
"\n",
"# Write more code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q1: Do the histograms look like the distributions for all 3 values of $p$? If not, what do you think is going on?**\n",
"\n",
"You'll notice that for $p=0.1$ the histogram and densities don't look quite the same -- the `hist()` function is lumping together the zeros and ones which makes it look off. This is typical for distributions that are truncated.\n",
"\n",
"#### Method of Moments (MoM) Estimators\n",
"\n",
"To obtain a method of moments estimator, we equate the theoretical moments (which will be a function of the parameters of the distribution) with the corresponding sample moments, and solve for the parameters in order to obtain an estimate. For the binomial distribution, there is only one parameter, $p$. \n",
"\n",
"**Q2: Given the analytic expected value, above, and assuming that the sample mean is $m$ (the mean number of observed heads across replicates), what is the MoM estimator for $p$?**\n",
"\n",
"Now calculate the MoM estimator for each of your 3 sets of simulated data sets to get the estimates for each of your values of $p$."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"## MOM estimators for 3 simulated sets\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q3: How good are your estimates for $p$? Do you get something close to the true value?**\n",
"\n",
"For 1 of your values of $p$, take 20 draws from the binomial with $N=20$ and calculate the MoM. Repeat this 100 times (hint: the `replicate()` and `lapply` functions may be useful.) Make a histogram of your estimates, and add a line/point to the plot to indicate the real value of $p$ that you used to simulate the data. "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"## MoM estimates, histogram "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q4: Is the MoM successfully estimating $p$? Does your histogram for $p$ look more or less normal? If so, what theorem might explain why this would be the case?** \n",
"\n",
"#### MLE for Binomial Distribution\n",
"\n",
"##### Likelihood and Log Likelihood\n",
"\n",
"Imagine that you flip a coin $N$ times, and then repeat the experiment $n$ times. Thus, you have data $x=x`1, x`2, \\dots x`n$ that are the number of times you observed a head in each trial. $p$ is the probability of obtaining a head. \n",
"\n",
"**Q5: Write down the likelihood and log-likelihood for the data. Take the derivative of the negative log-likelihood, set this equal to zero, and find the MLE, $\\hat{p}$.** \n",
"\n",
"\n",
"#### Computing the likelihood and MLE in R\n",
"\n",
"Simulate some data with $p=0.25$, $N=10$, and 10 replicates. Calculate the negative log-likelihood of your simulated data across a range of $p$ (from 0 to 1), and plot them. You may do this by using the built in functions in R (specifically `dbinom`) or write your own function. This is called a \"likelihood profile''. Plot your likelihood profile with a line indicating the true value of $p$. Add lines indicating the MLE $\\hat{p}$ and the MoM estimator for $p$ to your likelihood profile. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"pp<-.25\n",
"N<-10\n",
"reps<-10\n",
"## Make one set of data\n",
"\n",
"## the likelihood is always exactly zero\n",
"## at p=0,1, so I skip those values\n",
"ps<-seq(0.01, 0.99, by=0.01) \n",
"\n",
"## Likelihood\n",
"\n",
"\n",
"## MLE/MoM estimators \n",
"\n",
"## now plot the negative log likelihood profile\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q6: How does your MLE compare to the true parameter value? How could you estimate the MLE from the likelihood profile if you didn't have a way to calculate the MLE directly? If you chose another version of the random seed, do you get the same answer?**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example: Midge Wing Length\n",
"\n",
"We will use this simple example to go through the steps of assessing a Bayesian model and we'll see that MCMC can allow us to approximate the posterior distribution.\n",
"\n",
"Grogan and Wirth (1981) provide data on the wing length (in millimeters) of nine members of a species of midge (small, two-winged flies). \n",
"\n",
"From these measurements we wish to make inference about the population mean $\\mu$."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
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mu7XMxHpBIIKUM8Qtq+Zk2Z1/KpXSmE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\nAABJRU5ErkJggg==",
"text/plain": [
"Plot with title “Histogram of Y”"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"WL.data <- read.csv(\"../data/MidgeWingLength.csv\")\n",
"Y <- WL.data$WingLength\n",
"n <- length(Y)\n",
"\n",
"hist(Y,breaks=10,xlab=\"Wing Length (mm)\") "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Non-Bayesian analysis\n",
"\n",
"We might expect that these midge data could be draws from a _Normal_ distribution $\\mathcal{N}(\\mu, \\sigma^2)$. Recall that the MLEs for $\\mu$ and $\\sigma^2$ here are simply the _sample mean_ and _sample variance_ respectively:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<ol class=list-inline>\n",
"\t<li>1.804</li>\n",
"\t<li>0.017</li>\n",
"</ol>\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 1.804\n",
"\\item 0.017\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 1.804\n",
"2. 0.017\n",
"\n",
"\n"
],
"text/plain": [
"[1] 1.804 0.017"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m<-sum(Y)/n\n",
"s2<-sum((Y-m)^2)/(n-1)\n",
"round(c(m, s2), 3)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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NAEYQcAAKAJwg4AAEAThB0AAIAmCDsA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\nAAAATIJiBwAAYBL/B5KaVE7lPCR6AAAAAElFTkSuQmCC",
"text/plain": [
"Plot with title “Histogram of Y”"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x<-seq(1.4,2.2, length=50)\n",
"hist(Y,breaks=10,xlab=\"Wing Length (mm)\", xlim=c(1.4, 2.2), freq=FALSE) \n",
"lines(x, dnorm(x, mean=m, sd=sqrt(s2)), col=2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**NOTE:** I've plotted the estimate of the _population_ distribution here, but this is not the ***predictive distribution*** (which would be a Student T because we're estimating both the mean and variance...).\n",
"\n",
"-----\n",
"\n",
"The non-Bayesian version here has the advantage of being quick and familiar. However, from our point of view it has two weaknesses:\n",
"\n",
"1. Because we have so few data points estimates of the accuracy of our predictions aren't available. 9 points is only barely enough to estimate a mean, so we don't trust any of the variance calculations.\n",
"\n",
"2. We can't easily incorporate things that we might already know about midges into our analysis. \n",
"\n",
"Let's see how we can do a similar analysis using a Bayesian approach, first analytically, and the with JAGS.\n",
"\n",
"### Setting up the Bayesian Model\n",
"\n",
"We need to define the likelihood and the priors for our Bayesian analysis. Given the analysis that we've just done, let's assume that our data come from a normal distribution with unknown mean, $\\mu$ but that we know the variance is $\\sigma^2 = 0.025$. That is:\n",
"\n",
"$$\n",
"\\mathbf{Y} \\stackrel{\\mathrm{iid}}{\\sim} \\mathcal{N}(\\mu, 0.025^2)\n",
"$$\n",
"\n",
"\n",
"#### Prior Information\n",
"\n",
"Studies from other populations suggest that wing lengths are usually around 1.9 mm, so we set $\\mu_0 = 1.9$\n",
"\n",
"We also know that lengths must be positive ($\\mu >0$)\n",
"\n",
"We can approximate this restriction with a normal prior distribution for $\\mu$ as follows:\n",
"\n",
"Since most of the normal density is within two standard deviations of the mean we choose $\\tau^2_0$ so that\n",
"\n",
"$$ \\mu_0 - 2\\sigma_0 >0 \\Rightarrow \\sigma_0 <1.9/2 = 0.95 $$\n",
"I will choose $\\sigma_0=0.8$ here. Thus our prior for mu will be:\n",
"$$\n",
"\\mu \\sim \\mathcal{N}(1.9, 0.8^2)\n",
"$$\n",
"\n",
"----\n",
"\n",
"Together, then, our full model is:\n",
"\\begin{align*}\n",
"\\mathbf{Y} & \\stackrel{\\mathrm{iid}}{\\sim} \\mathcal{N}(\\mu, 0.025^2)\\\\\n",
"\\mu &\\sim \\mathcal{N}(1.9, 0.8^2)\n",
"\\end{align*}\n",
"\n",
"### Analytic Posterior\n",
"\n",
"For this very simple case it is easy to write down the posterior distribution (up to some constant). First, note that the likehood for the data can be written as \n",
"\n",
"\\begin{align*}\n",
"\\mathcal{L} &\\propto \\prod_{i=1}^n \\frac{1}{\\sigma} \\exp\\left(-\\frac{1}{2\\sigma^2}(Y_i-\\mu)^2 \\right) \\\\\n",
"& = \\frac{1}{\\sigma^n} \\exp\\left(-\\frac{1}{2\\sigma^2}\\sum_{i=1}^n (Y_i-\\mu)^2 \\right)\\\\\n",
"& \\propto \\exp\\left(-\\frac{n}{2\\sigma^2} (\\bar{Y}-\\mu)^2 \\right)\n",
"\\end{align*}\n",
"\n",
"Multiplying the prior through we get the following for the posterior:\n",
"\n",
"$$\n",
"\\mathrm{P}(\\mu|\\mathbf{Y}) \\propto \\exp \\left(-\\frac{n}{2\\sigma^2} (\\bar{Y}-\\mu)^2 \\right) \\exp\\left(-\\frac{1}{2\\sigma_0^2}(\\mu-\\mu_0)^2 \\right)\n",
"$$\n",
"\n",
"You can re-arrange, complete the square, etc, to get a new expression that is like\n",
"\n",
"$$\n",
"\\mathrm{P}(\\mu|\\mathbf{Y}) \\propto \\exp \\left(-\\frac{1}{2\\sigma_p^2} (\\mu_p-\\mu)^2 \\right)\n",
"$$\n",
"\n",
"where \n",
"\n",
"\\begin{align*}\n",
"\\mu_p & = \\frac{n\\sigma_0^2}{\\sigma^2 + n\\sigma_0^2} \\bar{Y} + \\frac{\\sigma^2}{\\frac{\\sigma^2}{n} + \\sigma_0^2} \\mu_0\\\\\n",
"& \\\\\n",
"\\sigma_p^2 & = \\left( \\frac{n}{\\sigma^2} + \\frac{1}{\\sigma_0^2} \\right)^{-1}\n",
"\\end{align*}\n",
"\n",
"Instead of writing this last in terms of the variances, we could instead use precision (the inverse variance) which gives a simpler expression:\n",
"\n",
"$$\n",
"\\tau_p = n\\tau + \\tau_0\n",
"$$\n",
"\n",
"Just like in our earlier example, our estimate of the mean is a weighted average of the data and the prior, with the variance being determined by the data and prior variances.\n",
"\n",
"So lets write a little function to calculate $\\mu_p$ and $\\tau_p$ and the plug in our numbers:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"tau.post<-function(tau, tau0, n){n*tau + tau0}\n",
"mu.post<-function(Ybar, mu0, sig20, sig2, n){\n",
" weight<-sig2+n*sig20\n",
" \n",
" return(n*sig20*Ybar/weight + sig2*mu0/weight)\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's plot 3 things together -- the data histogram, the prior, and the posterior:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"mu0 <- 1.9\n",
"s20 <- 0.8\n",
"s2<- 0.025 ## \"true\" variance\n",
"\n",
"mp<-mu.post(Ybar=m, mu0=mu0, sig20=s20, sig2=s2, n=n)\n",
"tp<-tau.post(tau=1/s2, tau0=1/s20, n=n)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's plot the result:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
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OKLo0ePXnrppY899ljnzp0HDRqUlpa2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\nsAMAALAIgh0AAIBFEOwAAAAs4v8DfC2Qj7nqk3YAAAAASUVORK5CYII=",
"text/plain": [
"Plot with title “Histogram of Y”"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x<-seq(1.3,2.3, length=1000)\n",
"hist(Y,breaks=10,xlab=\"Wing Length (mm)\", xlim=c(1.3, 2.3),\n",
" freq=FALSE, ylim=c(0,8)) \n",
"lines(x, dnorm(x, mean=mu0, sd=sqrt(s20)), col=2, lty=2, lwd=2) ## prior\n",
"lines(x, dnorm(x, mean=mp, sd=sqrt(1/tp)), col=4, lwd=2) ## posterior\n",
"legend(\"topleft\", legend=c(\"prior\", \"posterior\"), col=c(2,4), lty=c(2,1), lwd=2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise: Prior sensitivity\n",
"\n",
"Change the values of the mean and the variance that you choose for the prior (\"hyperparameters\"). What does this do to the posterior distribution. E.g., what happens if the variance you choose is small, and $\\mu_0 =2.5$ or so. Is this what you expect?\n",
"\n",
"\n",
"### Numerical evaluation of the posterior with JAGS\n",
"\n",
"Let's show that we can get the same thing from JAGS that we were able to get from the analytic results. You'll need to make sure you have installed JAGS (which must be done outside of R) and then the libraries `rjags` and `coda`."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"# Load libraries\n",
"require(rjags) # does the fitting\n",
"require(coda) # makes diagnostic plots\n",
"##require(mcmcplots) # another option for diagnostic plots"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Specifying the model\n",
"\n",
"First we must encode our choices for our data model and priors to pass them to the fitting routines in JAGS. This involves setting up a ${\\tt model}$ that includes the likelihood for each data point and a prior for every parameter we want to estimate. Here is an example of how we would do this for the simple model we fit for the midge data (note that JAGS uses the precision instead of the variance or sd for the normal distribution:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"model1 <- \"model{\n",
"\n",
" ## Likelihood\n",
" for(i in 1:n){\n",
" Y[i] ~ dnorm(mu,tau)\n",
" }\n",
"\n",
" ## Prior for mu\n",
" mu ~ dnorm(mu0,tau0)\n",
"\n",
"} ## close model \n",
"\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now create the JAGS model:"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"ename": "ERROR",
"evalue": "Error in jags.model(textConnection(model1), n.chains = 1, data = list(Y = Y, : could not find function \"jags.model\"\n",
"output_type": "error",
"traceback": [
"Error in jags.model(textConnection(model1), n.chains = 1, data = list(Y = Y, : could not find function \"jags.model\"\nTraceback:\n"
]
}
],
"source": [
"model <- jags.model(textConnection(model1), \n",
" n.chains = 1, ## usually do more\n",
" data = list(Y=Y,n=n, ## data\n",
" mu0=mu0, tau0=1/s20, ## hyperparams\n",
" tau = 1/s2 ## known precision\n",
" ),\n",
" inits=list(mu=3) ## setting an starting val\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we'll run the MCMC and, see how the output looks for a short chain with no burnin:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"samp <- coda.samples(model, \n",
" variable.names=c(\"mu\"), \n",
" n.iter=1000, progress.bar=\"none\")\n",
"\n",
"plot(samp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"MCMC is a rejection algorithm that often needs to converge or \"burn-in\" -- that is we need to potentially move until we're taking draws from the correct distribution. Unlike for optimization problems, this does not mean that the algorithm :eads toward a single value. Instead we're looking for a pattern where the draws are seemingly unrelated and random. To assess convergence we look at trace plots, the goal is to get traces that look like \"fuzzy caterpillars\". \n",
"\n",
"Sometimes at the beginning of a run, if we start far from the area near the posterior mean of the parameter, we will instead get something that looks like a trending time series. If this is the case we have to drop the samples that were taken during the burn-in phase. Here's an example of how to do that:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"update(model, 10000, progress.bar=\"none\") # Burnin for 10000 samples\n",
"\n",
"samp <- coda.samples(model, \n",
" variable.names=c(\"mu\"), \n",
" n.iter=20000, progress.bar=\"none\")\n",
"\n",
"plot(samp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is a very fuzzy caterpillar!\n",
"\n",
"We can also use the summary function to examine the samples generated:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"summary(samp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's compare these draws to what we got with our analytic solution:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"x<-seq(1.3,2.3, length=1000)\n",
"hist(samp[[1]], xlab=\"mu\", xlim=c(1.3, 2.3),\n",
" freq=FALSE, ylim=c(0,8), main =\"posterior samples\") \n",
"lines(x, dnorm(x, mean=mu0, sd=sqrt(s20)), col=2, lty=2, lwd=2) ## prior\n",
"lines(x, dnorm(x, mean=mp, sd=sqrt(1/tp)), col=4, lwd=2) ## posterior\n",
"legend(\"topleft\", legend=c(\"prior\", \"analytic posterior\"), col=c(2,4), lty=c(2,1), lwd=2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It worked! \n",
"\n",
"\n",
"As with the analytic approach, it's always a good idea when you run your analyses to see how sensitive is your result to the priors you choose. Unless you are purposefully choosing an informative prior, we usually want the prior and posterior to look different.\n",
"\n",
"\n",
"### Estimating the population variance\n",
" \n",
"One advantage of the numerical approach is that we can choose almost anything we want for the priors on multiple parameters without worrying if they are conjugate, or if we want to include additional information. For example, let's say that, not, we want to force the mean to be positive (and also the data, perhaps), and concurrently estimate the variance. Here is a possible model."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"model2 <- \"model{\n",
"\n",
" # Likelihood\n",
" for(i in 1:n){\n",
" Y[i] ~ dnorm(mu,tau) T(0,) ## truncates at 0\n",
" }\n",
"\n",
" # Prior for mu\n",
" mu ~ dnorm(mu0,tau0)\n",
"\n",
" # Prior for the precision\n",
" tau ~ dgamma(a, b)\n",
"\n",
" # Compute the variance\n",
" s2 <- 1/tau\n",
"}\"\n",
"\n",
"## hyperparams for tau\n",
"a <- 0.01\n",
"b <- 0.01\n",
"\n",
"m2 <- jags.model(textConnection(model2), \n",
" n.chains = 1,\n",
" data = list(Y=Y, n=n,\n",
" mu0=mu0, tau0=1/s20, ## mu hyperparams\n",
" a=a, b=b ## tau hyperparams\n",
" ),\n",
" inits=list(mu=3, tau=10) ## starting vals\n",
" )\n",
"\n",
"samp <- coda.samples(m2, \n",
" variable.names=c(\"mu\",\"s2\"), \n",
" n.iter=1000, progress.bar=\"none\")\n",
"\n",
"plot(samp)\n",
"\n",
"summary(samp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we plot each with their priors:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"ename": "ERROR",
"evalue": "Error in hist(samp[[1]][, 1], xlab = \"samples of mu\", main = \"mu\"): object 'samp' not found\n",
"output_type": "error",
"traceback": [
"Error in hist(samp[[1]][, 1], xlab = \"samples of mu\", main = \"mu\"): object 'samp' not found\nTraceback:\n",
"1. hist(samp[[1]][, 1], xlab = \"samples of mu\", main = \"mu\")"
]
}
],
"source": [
"par(mfrow=c(1,2), bty=\"n\")\n",
"\n",
"hist(samp[[1]][,1], xlab=\"samples of mu\", main=\"mu\")\n",
"lines(x, dnorm(x, mean=mu0, sd=sqrt(s20)), \n",
" col=2, lty=2, lwd=2) ## prior\n",
"\n",
"x2<-seq(0, 200, length=1000)\n",
"hist(1/samp[[1]][,2], xlab=\"samples of tau\", main=\"tau\")\n",
"lines(x2, dgamma(x2, shape = a, rate = b), \n",
" col=2, lty=2, lwd=2) ## prior"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We also want to look at the joint distribution of $\\mu$ and $\\sigma^2$:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plot(as.numeric(samp[[1]][,1]), samp[[1]][,2], xlab=\"mu\", ylab=\"s2\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise: Updating the Bayesian model\n",
"\n",
"Redo the previous analysis placing a gamma prior on $\\mu$ as well. Set the prior so that the mean and variance are the same as in the normal example from above (use moment matching). Do you get something similar?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Aedes data revisited using Bayesian fitting\n",
"\n",
"Now let's do some Bayesian model fitting to *Aedes* thermal performance data. Lets try out the `R2jags` package for this."
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Loading required package: R2jags\n",
"\n",
"Attaching package: ‘R2jags’\n",
"\n",
"The following object is masked from ‘package:coda’:\n",
"\n",
" traceplot\n",
"\n"
]
}
],
"source": [
"require(R2jags) # fitting\n",
"require(coda) # diagnostic plots\n",
"set.seed(1234)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Load the data:"
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {},
"outputs": [],
"source": [
"Aaeg.data <- read.csv(\"../data/AeaegyptiTraitData.csv\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### The Data\n",
"\n",
"These data are traits from *Aedes aegypti* mosquitoes measured across temperature in lab experiments. The traits we have data on thermal performance are:\n",
"- pEA: proportion surviving from egg to adulthood \n",
"- MDR: mosquito development rate \n",
"- PDR: parasite development rate (= 1/EIP the extrinsic incubation period) \n",
"- $\\mu$ (mu): death rate (= 1/longevity) \n",
"\n",
"Note that some of the traits come in multiple forms (e.g., $\\mu$ and 1/$\\mu$, PDR and EIP).\n",
"\n",
"Have a look at the data:"
]
},
{
"cell_type": "code",
"execution_count": 92,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<table>\n",
"<thead><tr><th scope=col>trait.name</th><th scope=col>T</th><th scope=col>trait</th><th scope=col>ref</th><th scope=col>trait2</th><th scope=col>trait2.name</th></tr></thead>\n",
"<tbody>\n",
"\t<tr><td>pEA </td><td>22 </td><td>0.90812 </td><td>Westbrook_Thesis_2010</td><td>NA </td><td>NA </td></tr>\n",
"\t<tr><td>pEA </td><td>27 </td><td>0.93590 </td><td>Westbrook_Thesis_2010</td><td>NA </td><td>NA </td></tr>\n",
"\t<tr><td>pEA </td><td>32 </td><td>0.81944 </td><td>Westbrook_Thesis_2010</td><td>NA </td><td>NA </td></tr>\n",
"\t<tr><td>MDR </td><td>22 </td><td>0.09174 </td><td>Westbrook_Thesis_2010</td><td>NA </td><td>NA </td></tr>\n",
"\t<tr><td>MDR </td><td>27 </td><td>0.13587 </td><td>Westbrook_Thesis_2010</td><td>NA </td><td>NA </td></tr>\n",
"\t<tr><td>MDR </td><td>32 </td><td>0.15823 </td><td>Westbrook_Thesis_2010</td><td>NA </td><td>NA </td></tr>\n",
"</tbody>\n",
"</table>\n"
],
"text/latex": [
"\\begin{tabular}{r|llllll}\n",
" trait.name & T & trait & ref & trait2 & trait2.name\\\\\n",
"\\hline\n",
"\t pEA & 22 & 0.90812 & Westbrook\\_Thesis\\_2010 & NA & NA \\\\\n",
"\t pEA & 27 & 0.93590 & Westbrook\\_Thesis\\_2010 & NA & NA \\\\\n",
"\t pEA & 32 & 0.81944 & Westbrook\\_Thesis\\_2010 & NA & NA \\\\\n",
"\t MDR & 22 & 0.09174 & Westbrook\\_Thesis\\_2010 & NA & NA \\\\\n",
"\t MDR & 27 & 0.13587 & Westbrook\\_Thesis\\_2010 & NA & NA \\\\\n",
"\t MDR & 32 & 0.15823 & Westbrook\\_Thesis\\_2010 & NA & NA \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"trait.name | T | trait | ref | trait2 | trait2.name | \n",
"|---|---|---|---|---|---|\n",
"| pEA | 22 | 0.90812 | Westbrook_Thesis_2010 | NA | NA | \n",
"| pEA | 27 | 0.93590 | Westbrook_Thesis_2010 | NA | NA | \n",
"| pEA | 32 | 0.81944 | Westbrook_Thesis_2010 | NA | NA | \n",
"| MDR | 22 | 0.09174 | Westbrook_Thesis_2010 | NA | NA | \n",
"| MDR | 27 | 0.13587 | Westbrook_Thesis_2010 | NA | NA | \n",
"| MDR | 32 | 0.15823 | Westbrook_Thesis_2010 | NA | NA | \n",
"\n",
"\n"
],
"text/plain": [
" trait.name T trait ref trait2 trait2.name\n",
"1 pEA 22 0.90812 Westbrook_Thesis_2010 NA NA \n",
"2 pEA 27 0.93590 Westbrook_Thesis_2010 NA NA \n",
"3 pEA 32 0.81944 Westbrook_Thesis_2010 NA NA \n",
"4 MDR 22 0.09174 Westbrook_Thesis_2010 NA NA \n",
"5 MDR 27 0.13587 Westbrook_Thesis_2010 NA NA \n",
"6 MDR 32 0.15823 Westbrook_Thesis_2010 NA NA "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"head(Aaeg.data)"
]
},
{
"cell_type": "code",
"execution_count": 93,
"metadata": {},
"outputs": [
{
"data": {
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5aKt1+vYjKCDgGcq5gkpDuFvqJdOPu2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\nnF4XF9aGd9YAAAAASUVORK5CYII=",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mu.data <- subset(Aaeg.data, trait.name == \"mu\")\n",
"lf.data <- subset(Aaeg.data, trait.name == \"1/mu\")\n",
"par(mfrow=c(1,2), bty=\"l\") \n",
"plot(trait ~ T, data = mu.data, ylab=\"mu\")\n",
"plot(trait ~ T, data = lf.data, ylab=\"1/mu\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that the $\\mu$ data is u-shaped and the lifespan data is unimodal (hump-shaped). \n",
"\n",
"Since thermal biology theory is based on unimodal thermal responses, we want to fit the trait as lifespan instead of $\\mu$. Thus, we'll need to convert the $\\mu$ data to lifespan by taking the inverse. The combined data should have a nice unimodal shape that we can fit a function to:"
]
},
{
"cell_type": "code",
"execution_count": 94,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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fHTV/vW+NTwc4OqPxslfnBo94v1B+u+ZHDCE8o2P3iT48Fp4207ybMrXuElQedH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\nhPL/j48s8MNS70sAAAAASUVORK5CYII=",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mu.data.inv <- mu.data # make a copy of the mu data\n",
"mu.data.inv$trait <- 1/mu.data$trait # take the inverse of the trait values to convert mu to lifespan\n",
"lf.data.comb <- rbind(mu.data.inv, lf.data) # combine both lifespan data sets together \n",
" \n",
"plot(trait ~ T, data = lf.data.comb, ylab=\"1/mu\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Two thermal performance curve models\n",
"Most thermal response curves can be reasonably fit using one of two thermal reponses. Traits that respond unimodally but symmetrically to temperature can be fit with a quadratic function:\n",
"\n",
"$ B = q (T-T_0) (T-T_m)$ \n",
"\n",
"Traits that respond unimodally but asymetrically can be fited with a Briere function:\n",
"\n",
"$B = q T (T-T_0) \\sqrt{T_m-T}$\n",
"\n",
"In both models, $T_0$ is the lower thermal limit, $T_m$ is the upper thermal limit (i.e., where the trait value goes to zero on either end), and $q$ scales the elevation of the curve, (and so also the value at the optimum temperature). \n",
"\n",
"\n",
"#### The thermal response model file\n",
"Unlike the previous bayesian \\example, here we will provide jags with the model written as a `.txt` file. THis can be in your working directory, or elsewhere (but then inout the full path to it --- ideally a relative path). \n",
"\n",
"You can either write the text yourself directly to the file, or create it using the sink() function via your R script (see below):"
]
},
{
"cell_type": "raw",
"metadata": {},
"source": [
"sink(\"../code/quad.txt\")\n",
"cat(\"\n",
" model{\n",
" \n",
" ## Priors\n",
" cf.q ~ dunif(0, 1)\n",
" cf.T0 ~ dunif(0, 24)\n",
" cf.Tm ~ dunif(25, 45)\n",
" cf.sigma ~ dunif(0, 1000)\n",
" cf.tau <- 1 / (cf.sigma * cf.sigma)\n",
" \n",
" ## Likelihood\n",
" for(i in 1:N.obs){\n",
" trait.mu[i] <- -1 * cf.q * (temp[i] - cf.T0) * (temp[i] - cf.Tm) * (cf.Tm > temp[i]) * (cf.T0 < temp[i])\n",
" trait[i] ~ dnorm(trait.mu[i], cf.tau)\n",
" }\n",
" \n",
" ## Derived Quantities and Predictions\n",
" for(i in 1:N.Temp.xs){\n",
" z.trait.mu.pred[i] <- -1 * cf.q * (Temp.xs[i] - cf.T0) * (Temp.xs[i] - cf.Tm) * (cf.Tm > Temp.xs[i]) * (cf.T0 < Temp.xs[i])\n",
" }\n",
" } # close model\n",
"\",fill=T)\n",
"sink()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that the model file `quad.txt` has two mandatory sections (the priors and the likelihood) and one optional section (derived measures calculated from your fitted parameters).\n",
"\n",
"In the example below for a quadratic function, most of the priors are specified via uniform distributions (the two arguments specific the lower and upper bounds, respectively). Note that unlike in R and most other programs, in jags, the inverse of the variance of the normal distribution is used, denoted by $\\tau (= \\frac{1}{\\sigma^2}$). \n",
"\n",
"The likelihood for can be interpreted as follows: the observed data are normally distributed where the mean at a given temperature follows the quadratic equation."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, prepare the data for jags: "
]
},
{
"cell_type": "code",
"execution_count": 101,
"metadata": {},
"outputs": [],
"source": [
"# Parameters to Estimate\n",
"parameters <- c(\"cf.q\", \"cf.T0\", \"cf.Tm\",\"cf.sigma\", \"z.trait.mu.pred\")\n",
"\n",
"# Initial values for the parameters\n",
"inits<-function(){list(\n",
" cf.q = 0.01,\n",
" cf.Tm = 35,\n",
" cf.T0 = 5,\n",
" cf.sigma = rlnorm(1))}\n",
"\n",
"# MCMC Settings: number of posterior dist elements = [(ni - nb) / nt ] * nc\n",
"ni <- 25000 # number of iterations in each chain\n",
"nb <- 5000 # number of 'burn in' iterations to discard\n",
"nt <- 8 # thinning rate - jags saves every nt iterations in each chain\n",
"nc <- 3 # number of chains\n",
"\n",
"# Temperature sequence for derived quantity calculations\n",
"Temp.xs <- seq(0, 45, 0.2)\n",
"N.Temp.xs <-length(Temp.xs)\n",
"\n",
"### Fitting the trait thermal response; Pull out data columns as vectors\n",
"data <- lf.data.comb # this lets us reuse the same generic code: we only change this first line\n",
"trait <- data$trait\n",
"N.obs <- length(trait)\n",
"temp <- data$T\n",
"\n",
"# Bundle all data in a list for JAGS\n",
"jag.data<-list(trait = trait, N.obs = N.obs, temp = temp, Temp.xs = Temp.xs, N.Temp.xs = N.Temp.xs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now run the fitting using jags:"
]
},
{
"cell_type": "code",
"execution_count": 102,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Warning message in file(modfile, \"rt\"):\n",
"“cannot open file 'quad.txt': No such file or directory”"
]
},
{
"ename": "ERROR",
"evalue": "Error in jags.model(model.file, data = data, inits = init.values, n.chains = n.chains, : Cannot open model file \"quad.txt\"\n",
"output_type": "error",
"traceback": [
"Error in jags.model(model.file, data = data, inits = init.values, n.chains = n.chains, : Cannot open model file \"quad.txt\"\nTraceback:\n",
"1. jags(data = jag.data, inits = inits, parameters.to.save = parameters, \n . model.file = \"quad.txt\", n.thin = nt, n.chains = nc, n.burnin = nb, \n . n.iter = ni, DIC = T, working.directory = getwd())",
"2. jags.model(model.file, data = data, inits = init.values, n.chains = n.chains, \n . n.adapt = 0)",
"3. stop(paste(\"Cannot open model file \\\"\", modfile, \"\\\"\", sep = \"\"))"
]
}
],
"source": [
"lf.fit <- jags(data=jag.data, inits=inits, parameters.to.save=parameters, \n",
" model.file=\"quad.txt\", n.thin=nt, n.chains=nc, n.burnin=nb, \n",
" n.iter=ni, DIC=T, working.directory=getwd())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Change into \"mcmc\" type samples for visualization with the `coda` package:"
]
},
{
"cell_type": "code",
"execution_count": 117,
"metadata": {},
"outputs": [],
"source": [
"lf.fit.mcmc <- as.mcmc(lf.fit)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Running diagnostics\n",
"\n",
"View the parameters (only the first 5 lines, or it will also show you all of your derived quantities):"
]
},
{
"cell_type": "code",
"execution_count": 118,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<table>\n",
"<thead><tr><th></th><th scope=col>mean</th><th scope=col>sd</th><th scope=col>2.5%</th><th scope=col>25%</th><th scope=col>50%</th><th scope=col>75%</th><th scope=col>97.5%</th><th scope=col>Rhat</th><th scope=col>n.eff</th></tr></thead>\n",
"<tbody>\n",
"\t<tr><th scope=row>cf.T0</th><td> 6.4943265 </td><td>2.09300384 </td><td> 1.60602110</td><td> 5.24712819</td><td> 6.7642097 </td><td> 7.960755 </td><td> 9.8890203 </td><td>1.011800 </td><td> 450 </td></tr>\n",
"\t<tr><th scope=row>cf.Tm</th><td> 39.2489169 </td><td>1.66643065 </td><td> 36.56998429</td><td> 38.04932891</td><td> 39.0173139 </td><td> 40.200410 </td><td> 43.1551656 </td><td>1.004244 </td><td> 580 </td></tr>\n",
"\t<tr><th scope=row>cf.q</th><td> 0.1099374 </td><td>0.02623226 </td><td> 0.06461983</td><td> 0.09123192</td><td> 0.1085517 </td><td> 0.126104 </td><td> 0.1657431 </td><td>1.005886 </td><td> 440 </td></tr>\n",
"\t<tr><th scope=row>cf.sigma</th><td> 6.7100226 </td><td>0.96797653 </td><td> 5.13196346</td><td> 6.03242714</td><td> 6.6036237 </td><td> 7.279794 </td><td> 8.9213322 </td><td>1.001077 </td><td>7200 </td></tr>\n",
"\t<tr><th scope=row>deviance</th><td>197.7198535 </td><td>3.09086985 </td><td>193.77713702</td><td>195.42279657</td><td>197.0587314 </td><td>199.288979 </td><td>205.4720801 </td><td>1.001325 </td><td>3800 </td></tr>\n",
"</tbody>\n",
"</table>\n"
],
"text/latex": [
"\\begin{tabular}{r|lllllllll}\n",
" & mean & sd & 2.5\\% & 25\\% & 50\\% & 75\\% & 97.5\\% & Rhat & n.eff\\\\\n",
"\\hline\n",
"\tcf.T0 & 6.4943265 & 2.09300384 & 1.60602110 & 5.24712819 & 6.7642097 & 7.960755 & 9.8890203 & 1.011800 & 450 \\\\\n",
"\tcf.Tm & 39.2489169 & 1.66643065 & 36.56998429 & 38.04932891 & 39.0173139 & 40.200410 & 43.1551656 & 1.004244 & 580 \\\\\n",
"\tcf.q & 0.1099374 & 0.02623226 & 0.06461983 & 0.09123192 & 0.1085517 & 0.126104 & 0.1657431 & 1.005886 & 440 \\\\\n",
"\tcf.sigma & 6.7100226 & 0.96797653 & 5.13196346 & 6.03242714 & 6.6036237 & 7.279794 & 8.9213322 & 1.001077 & 7200 \\\\\n",
"\tdeviance & 197.7198535 & 3.09086985 & 193.77713702 & 195.42279657 & 197.0587314 & 199.288979 & 205.4720801 & 1.001325 & 3800 \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| <!--/--> | mean | sd | 2.5% | 25% | 50% | 75% | 97.5% | Rhat | n.eff | \n",
"|---|---|---|---|---|\n",
"| cf.T0 | 6.4943265 | 2.09300384 | 1.60602110 | 5.24712819 | 6.7642097 | 7.960755 | 9.8890203 | 1.011800 | 450 | \n",
"| cf.Tm | 39.2489169 | 1.66643065 | 36.56998429 | 38.04932891 | 39.0173139 | 40.200410 | 43.1551656 | 1.004244 | 580 | \n",
"| cf.q | 0.1099374 | 0.02623226 | 0.06461983 | 0.09123192 | 0.1085517 | 0.126104 | 0.1657431 | 1.005886 | 440 | \n",
"| cf.sigma | 6.7100226 | 0.96797653 | 5.13196346 | 6.03242714 | 6.6036237 | 7.279794 | 8.9213322 | 1.001077 | 7200 | \n",
"| deviance | 197.7198535 | 3.09086985 | 193.77713702 | 195.42279657 | 197.0587314 | 199.288979 | 205.4720801 | 1.001325 | 3800 | \n",
"\n",
"\n"
],
"text/plain": [
" mean sd 2.5% 25% 50% \n",
"cf.T0 6.4943265 2.09300384 1.60602110 5.24712819 6.7642097\n",
"cf.Tm 39.2489169 1.66643065 36.56998429 38.04932891 39.0173139\n",
"cf.q 0.1099374 0.02623226 0.06461983 0.09123192 0.1085517\n",
"cf.sigma 6.7100226 0.96797653 5.13196346 6.03242714 6.6036237\n",
"deviance 197.7198535 3.09086985 193.77713702 195.42279657 197.0587314\n",
" 75% 97.5% Rhat n.eff\n",
"cf.T0 7.960755 9.8890203 1.011800 450 \n",
"cf.Tm 40.200410 43.1551656 1.004244 580 \n",
"cf.q 0.126104 0.1657431 1.005886 440 \n",
"cf.sigma 7.279794 8.9213322 1.001077 7200 \n",
"deviance 199.288979 205.4720801 1.001325 3800 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lf.fit$BUGSoutput$summary[1:5,]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot the chains:"
]
},
{
"cell_type": "code",
"execution_count": 119,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
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3K9lFsbx3OQyWaqiRrCBTImJkkWfaf/nUfFDh9W5m8S1xBHZUV1d+v+6BlpPI+H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\nNBwAAADAOTQcAAAAwDk0HAAAAMC5/wGW0K2aijdhfwAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title “Density of cf.Tm”"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(lf.fit.mcmc[,c(1,3,4)])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Plot the fits"
]
},
{
"cell_type": "code",
"execution_count": 120,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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p/zGYxR6qL3WMZjAeuo/KFNKeoqwhhJLRrdK84f2LjH9E6hDK3eOc1jClr0sopG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\nU8ssjDVujGqHVf5upbBPVs9o7LpDV536snB3zmvlNtx9eaCVjwd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IdfLcVfRsxjbDVOw/m5lhk4VciDyh+/D/hqjZnjitF0sDYCQ0K5fC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\nIAoQGiAKEBogChAaIAoQGiAKEBogiv8DbzzzSNp/Vi0AAAAASUVORK5CYII=",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(trait ~ T, xlim = c(0, 45), ylim = c(0,42), data = lf.data.comb, ylab = \"Lifespan for Ae. aegypti\", xlab = \"Temperature\")\n",
"lines(lf.fit$BUGSoutput$summary[6:(6 + N.Temp.xs - 1), \"2.5%\"] ~ Temp.xs, lty = 2)\n",
"lines(lf.fit$BUGSoutput$summary[6:(6 + N.Temp.xs - 1), \"97.5%\"] ~ Temp.xs, lty = 2)\n",
"lines(lf.fit$BUGSoutput$summary[6:(6 + N.Temp.xs - 1), \"mean\"] ~ Temp.xs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Additional analyses\n",
"\n",
"You can use the `which.max()` function to find the optimal temperature for adult lifespan:"
]
},
{
"cell_type": "code",
"execution_count": 121,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"23"
],
"text/latex": [
"23"
],
"text/markdown": [
"23"
],
"text/plain": [
"[1] 23"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Temp.xs[which.max(as.vector(lf.fit$BUGSoutput$summary[6:(6 + N.Temp.xs - 1), \"mean\"]))]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can also pull out the lifespan values for each iteration of the MCMC chain over the temperature gradient to calculate $R_0$:"
]
},
{
"cell_type": "code",
"execution_count": 122,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/html": [
"<ol class=list-inline>\n",
"\t<li>7500</li>\n",
"\t<li>226</li>\n",
"</ol>\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 7500\n",
"\\item 226\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 7500\n",
"2. 226\n",
"\n",
"\n"
],
"text/plain": [
"[1] 7500 226"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lf.grad <- lf.fit$BUGSoutput$sims.list$z.trait.mu.pred\n",
"dim(lf.grad) # A matrix with 7500 iterations of the MCMC chains at 226 temperatures"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### A Bayesian model fitting of abundance data\n",
"\n",
"We will now perform a bayesian analysis of population growth data. "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Loading required package: R2jags\n",
"Loading required package: rjags\n",
"Loading required package: coda\n",
"Linked to JAGS 4.2.0\n",
"Loaded modules: basemod,bugs\n",
"\n",
"Attaching package: ‘R2jags’\n",
"\n",
"The following object is masked from ‘package:coda’:\n",
"\n",
" traceplot\n",
"\n",
"Loading required package: grid\n",
"Loading required package: lattice\n"
]
}
],
"source": [
"require(R2jags) # does the fitting\n",
"require(coda) # makes diagnostic plots\n",
"library(IDPmisc) # makes nice colored pairs plots to look at joint posteriors"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### The Data\n",
"\n",
"These data are observations of the amphibian fungal pathogen _Batrachochytrium dendrobatidis_ being grown in liquid culture at multiple different temperatures. The experiment is conducted in 96 well plates with a fixed initial innoculation of fungal spores in each well, and the plate placed in a constant temperature incubator. Each day, 8 wells per plate are observed and the optical density (OD) is measured. We will focus on a single temperature trial across mulitple plates with OD as the response. \n",
"\n",
"We will fit a logistic model to these growth data. \n",
"\n",
"Let's have a look at the data first:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<table>\n",
"<thead><tr><th scope=col>X</th><th scope=col>EXP</th><th scope=col>TEMP</th><th scope=col>DAY</th><th scope=col>ISOLATE</th><th scope=col>PLATE</th><th scope=col>WELL</th><th scope=col>OD</th><th scope=col>NC_AVG</th><th scope=col>OD_SUB</th></tr></thead>\n",
"<tbody>\n",
"\t<tr><td>1 </td><td>2 </td><td>5 </td><td>1 </td><td>LB_AB </td><td>P.16 </td><td>1 </td><td>0.120 </td><td>0.1195</td><td>0.0005</td></tr>\n",
"\t<tr><td>2 </td><td>2 </td><td>5 </td><td>1 </td><td>LB_AB </td><td>P.16 </td><td>2 </td><td>0.120 </td><td>0.1195</td><td>0.0005</td></tr>\n",
"\t<tr><td>3 </td><td>2 </td><td>5 </td><td>1 </td><td>LB_AB </td><td>P.16 </td><td>3 </td><td>0.122 </td><td>0.1195</td><td>0.0025</td></tr>\n",
"\t<tr><td>4 </td><td>2 </td><td>5 </td><td>1 </td><td>LB_AB </td><td>P.16 </td><td>4 </td><td>0.123 </td><td>0.1195</td><td>0.0035</td></tr>\n",
"\t<tr><td>5 </td><td>2 </td><td>5 </td><td>1 </td><td>LB_AB </td><td>P.16 </td><td>5 </td><td>0.125 </td><td>0.1195</td><td>0.0055</td></tr>\n",
"\t<tr><td>6 </td><td>2 </td><td>5 </td><td>1 </td><td>LB_AB </td><td>P.16 </td><td>6 </td><td>0.125 </td><td>0.1195</td><td>0.0055</td></tr>\n",
"</tbody>\n",
"</table>\n"
],
"text/latex": [
"\\begin{tabular}{r|llllllllll}\n",
" X & EXP & TEMP & DAY & ISOLATE & PLATE & WELL & OD & NC\\_AVG & OD\\_SUB\\\\\n",
"\\hline\n",
"\t 1 & 2 & 5 & 1 & LB\\_AB & P.16 & 1 & 0.120 & 0.1195 & 0.0005 \\\\\n",
"\t 2 & 2 & 5 & 1 & LB\\_AB & P.16 & 2 & 0.120 & 0.1195 & 0.0005 \\\\\n",
"\t 3 & 2 & 5 & 1 & LB\\_AB & P.16 & 3 & 0.122 & 0.1195 & 0.0025 \\\\\n",
"\t 4 & 2 & 5 & 1 & LB\\_AB & P.16 & 4 & 0.123 & 0.1195 & 0.0035 \\\\\n",
"\t 5 & 2 & 5 & 1 & LB\\_AB & P.16 & 5 & 0.125 & 0.1195 & 0.0055 \\\\\n",
"\t 6 & 2 & 5 & 1 & LB\\_AB & P.16 & 6 & 0.125 & 0.1195 & 0.0055 \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"X | EXP | TEMP | DAY | ISOLATE | PLATE | WELL | OD | NC_AVG | OD_SUB | \n",
"|---|---|---|---|---|---|\n",
"| 1 | 2 | 5 | 1 | LB_AB | P.16 | 1 | 0.120 | 0.1195 | 0.0005 | \n",
"| 2 | 2 | 5 | 1 | LB_AB | P.16 | 2 | 0.120 | 0.1195 | 0.0005 | \n",
"| 3 | 2 | 5 | 1 | LB_AB | P.16 | 3 | 0.122 | 0.1195 | 0.0025 | \n",
"| 4 | 2 | 5 | 1 | LB_AB | P.16 | 4 | 0.123 | 0.1195 | 0.0035 | \n",
"| 5 | 2 | 5 | 1 | LB_AB | P.16 | 5 | 0.125 | 0.1195 | 0.0055 | \n",
"| 6 | 2 | 5 | 1 | LB_AB | P.16 | 6 | 0.125 | 0.1195 | 0.0055 | \n",
"\n",
"\n"
],
"text/plain": [
" X EXP TEMP DAY ISOLATE PLATE WELL OD NC_AVG OD_SUB\n",
"1 1 2 5 1 LB_AB P.16 1 0.120 0.1195 0.0005\n",
"2 2 2 5 1 LB_AB P.16 2 0.120 0.1195 0.0005\n",
"3 3 2 5 1 LB_AB P.16 3 0.122 0.1195 0.0025\n",
"4 4 2 5 1 LB_AB P.16 4 0.123 0.1195 0.0035\n",
"5 5 2 5 1 LB_AB P.16 5 0.125 0.1195 0.0055\n",
"6 6 2 5 1 LB_AB P.16 6 0.125 0.1195 0.0055"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dat <- read.csv(\"../data/lb_ab_temps.csv\")\n",
"head(dat)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are only interested in a subset of these data, so we will subset out only those from experiment 2, and a temperature of 12$^\\circ$C."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" EXP TEMP DAY ISOLATE PLATE \n",
" Min. :2 Min. :12 Min. : 1.00 LB_AB:730 P.11 :160 \n",
" 1st Qu.:2 1st Qu.:12 1st Qu.: 9.00 P.12 :150 \n",
" Median :2 Median :12 Median :19.00 P.13 :150 \n",
" Mean :2 Mean :12 Mean :19.04 P.14 :140 \n",
" 3rd Qu.:2 3rd Qu.:12 3rd Qu.:29.00 P.15 :130 \n",
" Max. :2 Max. :12 Max. :39.00 P.1 : 0 \n",
" (Other): 0 \n",
" WELL OD \n",
" Min. :1.000 Min. :0.0930 \n",
" 1st Qu.:2.000 1st Qu.:0.1630 \n",
" Median :4.000 Median :0.2580 \n",
" Mean :4.315 Mean :0.2437 \n",
" 3rd Qu.:6.000 3rd Qu.:0.3170 \n",
" Max. :8.000 Max. :0.4600 \n",
" "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"d2<-dat[which(dat$EXP==2),2:8]\n",
"d2<-d2[which(d2$TEMP==12),]\n",
"summary(d2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now plot it:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
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b097OxQpAg++AAnT2Z2WQCAHTtQqRIaN8aZM+jZE1ottm/HokVYtgyRkfD1RXg4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\nbgAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title “LB-AB isolate, T=12C”"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Temps<-seq(0,max(d2$DAY)-1, by=0.05)\n",
"mycol<-1 \n",
"my.ylim<-c(0, 0.5)\n",
"my.title<-\"LB-AB isolate, T=12C\"\n",
"\n",
"plot(d2$DAY-1, d2$OD, xlim=c(0,max(Temps)), ylim=my.ylim,\n",
" pch=(mycol+20),\n",
" xlab=\"time (days)\", ylab=\"\",\n",
" main=my.title,\n",
" col=mycol+1, cex=1.5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Specifying the growth curve\n",
"\n",
"Although logistic growth is often written as a differential equation, here we will work with the analytic solution of the model:\n",
"\n",
"$$\n",
"\\mu(t) = \\frac{KY_0}{Y_0+(K-Y_0)\\exp{(-rt)}}\n",
"$$\n",
"\n",
"This gives the mean function that we want to fit. We will assume log-normal noise around this response, as the optical density is bounded to be greater than 0 and since we also have increasing variance over time (as the optical density increases).\n",
"\n",
"\n",
"#### The thermal response model file\n",
"\n",
"JAGS needs the model written as a `.txt` or `.bug` file inside the working directory. You can either make the text file directly, or create it using the `sink()` function in your R script, as follows: "
]
},
{
"cell_type": "raw",
"metadata": {},
"source": [
"sink(\"jags-logistic.bug\")\n",
"cat(\"\n",
" model {\n",
" \n",
" ## Likelihood\n",
" for (i in 1:N) {\n",
" Y[i] ~ dlnorm(log(mu[i]), tau)\n",
" mu[i] <- K*Y0/(Y0+(K-Y0)*exp(-r*t[i]))\n",
" }\n",
"\n",
" ## Priors\n",
" r~dexp(1000)\n",
" K ~ dunif(0.01, 0.6)\n",
" Y0 ~ dunif(0.09, 0.15)\n",
" tau<-1/sigma^2\n",
" sigma ~ dexp(0.1)\n",
"\n",
" } # close model\n",
" \",fill=T)\n",
"sink()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that the model file has two mandatory sections (the priors and the likelihood) and one optional section (derived quantiaties calculated from your fitted parameters). \n",
"\n",
"In the example below we will build the model function with the log-normal likelihood for the logistic growth function. Priors are a combination of uniform and exponential distributions. As with the normal distribution, jags uses $\\tau$ to parameterize the variance of the normal distribution ($\\tau = 1/(\\sigma^2)$). However it can be easier to specify the prior on sigma directly. In this example we will generate posterior samples of derived quantities outside of JAGS (so you can see what this is actually doing).\n",
"\n",
"\n",
"#### Additional settings for jags \n",
"\n",
"Now for some additional settings/specifications for jags:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"# Parameters to Estimate\n",
"parameters <- c('Y0', 'K', 'r', 'sigma')\n",
"\n",
"# Initial values for the parameters\n",
"inits<-function(){list(\n",
" Y0 = 0.1,\n",
" K = 0.4,\n",
" r = 0.1,\n",
" sigma = rlnorm(1))}\n",
"\n",
"# MCMC Settings: number of posterior dist elements = [(ni - nb) / nt ] * nc\n",
"ni <- 6000 # number of iterations in each chain\n",
"nb <- 1000 # number of 'burn in' iterations to discard\n",
"nt <- 1 # thinning rate - jags saves every nt iterations in each chain\n",
"nc <- 5 # number of chains"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Fitting the model\n",
"\n",
"Now we can run jags:"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"module glm loaded\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Compiling model graph\n",
" Resolving undeclared variables\n",
" Allocating nodes\n",
"Graph information:\n",
" Observed stochastic nodes: 730\n",
" Unobserved stochastic nodes: 4\n",
" Total graph size: 1598\n",
"\n",
"Initializing model\n",
"\n"
]
}
],
"source": [
"# Pull out data columns as vectors\n",
"data <- d2 # this lets us reuse the same generic code: we only change this first line\n",
"Y <- data$OD\n",
"N <- length(Y)\n",
"t <- data$DAY\n",
"\n",
"# Bundle all data in a list for JAGS\n",
"jag.data<-list(Y = Y, N = N, t = t)\n",
"\n",
"# Run JAGS\n",
"OD.12C <- jags(data=jag.data, inits=inits, parameters.to.save=parameters, \n",
" model.file=\"jags-logistic.bug\", n.thin=nt, n.chains=nc, n.burnin=nb, \n",
" n.iter=ni, DIC=T, working.directory=getwd())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Change into \"mcmc\" type samples for visualization with `coda`:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"OD.12C.mcmc<-as.mcmc(OD.12C)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Diagnostics\n",
"\n",
"As you did in the [Traits bayesian fitting example](#Aedes-data-revisited-using-Bayesian-fitting), there are a number of model diagnostics that we need to check. First we want to look at the chains and confirm that they look like \"fuzzy caterpillars\" -- no linear/non-linear patterns across the chains, low auto-correlation, etc.\n",
"\n",
"First view the fitted parameters:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<table>\n",
"<thead><tr><th></th><th scope=col>mean</th><th scope=col>sd</th><th scope=col>2.5%</th><th scope=col>25%</th><th scope=col>50%</th><th scope=col>75%</th><th scope=col>97.5%</th><th scope=col>Rhat</th><th scope=col>n.eff</th></tr></thead>\n",
"<tbody>\n",
"\t<tr><th scope=row>K</th><td> 3.659490e-01</td><td>0.0055513205 </td><td> 3.552925e-01</td><td> 3.622170e-01</td><td> 3.658641e-01</td><td> 3.696170e-01</td><td> 3.772298e-01</td><td>1.001300 </td><td> 7500 </td></tr>\n",
"\t<tr><th scope=row>Y0</th><td> 9.051409e-02</td><td>0.0004844611 </td><td> 9.001452e-02</td><td> 9.015819e-02</td><td> 9.037434e-02</td><td> 9.072057e-02</td><td> 9.179751e-02</td><td>1.001085 </td><td>16000 </td></tr>\n",
"\t<tr><th scope=row>deviance</th><td>-2.823094e+03</td><td>6.0822395330 </td><td>-2.832126e+03</td><td>-2.827586e+03</td><td>-2.824031e+03</td><td>-2.819654e+03</td><td>-2.808733e+03</td><td>1.001097 </td><td>15000 </td></tr>\n",
"\t<tr><th scope=row>r</th><td> 1.051490e-01</td><td>0.0023217883 </td><td> 1.005654e-01</td><td> 1.035754e-01</td><td> 1.051368e-01</td><td> 1.067121e-01</td><td> 1.097114e-01</td><td>1.001249 </td><td> 8600 </td></tr>\n",
"\t<tr><th scope=row>sigma</th><td> 1.563601e-01</td><td>0.0041764147 </td><td> 1.484153e-01</td><td> 1.535103e-01</td><td> 1.562650e-01</td><td> 1.591003e-01</td><td> 1.647488e-01</td><td>1.001038 </td><td>22000 </td></tr>\n",
"</tbody>\n",
"</table>\n"
],
"text/latex": [
"\\begin{tabular}{r|lllllllll}\n",
" & mean & sd & 2.5\\% & 25\\% & 50\\% & 75\\% & 97.5\\% & Rhat & n.eff\\\\\n",
"\\hline\n",
"\tK & 3.659490e-01 & 0.0055513205 & 3.552925e-01 & 3.622170e-01 & 3.658641e-01 & 3.696170e-01 & 3.772298e-01 & 1.001300 & 7500 \\\\\n",
"\tY0 & 9.051409e-02 & 0.0004844611 & 9.001452e-02 & 9.015819e-02 & 9.037434e-02 & 9.072057e-02 & 9.179751e-02 & 1.001085 & 16000 \\\\\n",
"\tdeviance & -2.823094e+03 & 6.0822395330 & -2.832126e+03 & -2.827586e+03 & -2.824031e+03 & -2.819654e+03 & -2.808733e+03 & 1.001097 & 15000 \\\\\n",
"\tr & 1.051490e-01 & 0.0023217883 & 1.005654e-01 & 1.035754e-01 & 1.051368e-01 & 1.067121e-01 & 1.097114e-01 & 1.001249 & 8600 \\\\\n",
"\tsigma & 1.563601e-01 & 0.0041764147 & 1.484153e-01 & 1.535103e-01 & 1.562650e-01 & 1.591003e-01 & 1.647488e-01 & 1.001038 & 22000 \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| <!--/--> | mean | sd | 2.5% | 25% | 50% | 75% | 97.5% | Rhat | n.eff | \n",
"|---|---|---|---|---|\n",
"| K | 3.659490e-01 | 0.0055513205 | 3.552925e-01 | 3.622170e-01 | 3.658641e-01 | 3.696170e-01 | 3.772298e-01 | 1.001300 | 7500 | \n",
"| Y0 | 9.051409e-02 | 0.0004844611 | 9.001452e-02 | 9.015819e-02 | 9.037434e-02 | 9.072057e-02 | 9.179751e-02 | 1.001085 | 16000 | \n",
"| deviance | -2.823094e+03 | 6.0822395330 | -2.832126e+03 | -2.827586e+03 | -2.824031e+03 | -2.819654e+03 | -2.808733e+03 | 1.001097 | 15000 | \n",
"| r | 1.051490e-01 | 0.0023217883 | 1.005654e-01 | 1.035754e-01 | 1.051368e-01 | 1.067121e-01 | 1.097114e-01 | 1.001249 | 8600 | \n",
"| sigma | 1.563601e-01 | 0.0041764147 | 1.484153e-01 | 1.535103e-01 | 1.562650e-01 | 1.591003e-01 | 1.647488e-01 | 1.001038 | 22000 | \n",
"\n",
"\n"
],
"text/plain": [
" mean sd 2.5% 25% 50% \n",
"K 3.659490e-01 0.0055513205 3.552925e-01 3.622170e-01 3.658641e-01\n",
"Y0 9.051409e-02 0.0004844611 9.001452e-02 9.015819e-02 9.037434e-02\n",
"deviance -2.823094e+03 6.0822395330 -2.832126e+03 -2.827586e+03 -2.824031e+03\n",
"r 1.051490e-01 0.0023217883 1.005654e-01 1.035754e-01 1.051368e-01\n",
"sigma 1.563601e-01 0.0041764147 1.484153e-01 1.535103e-01 1.562650e-01\n",
" 75% 97.5% Rhat n.eff\n",
"K 3.696170e-01 3.772298e-01 1.001300 7500\n",
"Y0 9.072057e-02 9.179751e-02 1.001085 16000\n",
"deviance -2.819654e+03 -2.808733e+03 1.001097 15000\n",
"r 1.067121e-01 1.097114e-01 1.001249 8600\n",
"sigma 1.591003e-01 1.647488e-01 1.001038 22000"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"OD.12C$BUGSoutput$summary"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot the chains using the coda package:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
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Rua+vefsm7divPnpXe9lbYlyeVz0xkIlc3KmZjzm89vMhmcnaEDrO1Dom7etA04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+JTjMVzPlCCGEEELUhXqtCSGEEKJylHAQ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\nYZrlK6DSi+Mq+z6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OCFmyZMtB7KFz5Kj6zL5SZxOs73yEicf1z4UhsPAEXPW9jx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\ns/t/xHAGw3wgej4AAAAASUVORK5CYII=",
"text/plain": [
"Plot with title “Density of sigma”"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(OD.12C.mcmc[,c(1,2,4)])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can examine the ACF of the chains as well, similarly to a time series:"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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zyk+GdXr15dv379kSNHjI5KkvT2229PnTq1Q4cOplaIj4/38/OztbU1tUJ8fHxA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\nAAAASUVORK5CYII=",
"text/plain": [
"Plot with title “Series s1[, i]”"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"s1<-as.data.frame(OD.12C.mcmc[[1]])\n",
"par(mfrow=c(2,2))\n",
"for(i in 2:5) acf(s1[,i], lag.max=20)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is still a bit of autocorrelation, but it isn't too bad. The chain for $\\sigma$ is mixing best. We could reduce the autocorrelation even further by thinning the chain (i.e., change the `nt` parameter to 5 or 10).\n",
"\n",
"The last important diagnostic is to compare the prior and posterior distributions. Various packages in R have bespoke functions to do this. Here we use functions that we provide in the `mcmc_utils.R` file provided on the website."
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [],
"source": [
"source(\"../code/mcmc_utils.R\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We also can write a function to put the samples into a convenient format for visualizing, etc:"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [],
"source": [
"samps<-NULL\n",
"for(i in 1:nc){\n",
" samps<-rbind(samps, as.data.frame(OD.12C.mcmc[[i]]))\n",
"}\n",
"\n",
"samps<-samps[,c(5,2,3,4)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And also, we can building a list to hold all the information about the priors for each parameter:"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [],
"source": [
"priors<-list()\n",
"priors$names<-c(\"Y0\", \"K\", \"r\",\"sigma\")\n",
"priors$fun<-c(\"uniform\", \"uniform\", \"exp\",\"exp\")\n",
"priors$hyper<-matrix(NA, ncol=4, nrow=3)\n",
"priors$hyper[,1]<-c(0.09, 0.15, NA)\n",
"priors$hyper[,2]<-c(0.01, 0.6, NA)\n",
"priors$hyper[,3]<-c(1000, NA, NA) \n",
"priors$hyper[,4]<-c(0.1, NA, NA)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can plot the histograms of the posterior samples together with the prior distributions:"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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bNmMiQGAADWYosLf61evXrevHn32cHH\nx+eh8wEAAPXY4sJfc+fOlao2bty4p556Sq7YAADAClj4CwAAKI6FvwAAgOJY+AsAAChO5oW/\nTCaTvb29Xq/X6/WlpaWbNm1KSkry8vIKCAho0EDmYwEAgNpCtptGS0pKpk2b5uzs3LRp07Cw\nMJPJNG7cOKPRGB4ePnTo0H79+l25ckWuYwEAgNpFtsKxZMmSzz77bNKkSQsWLNi+fXvv3r33\n7Nmzd+/e69evJycnnzhxYtGiRXIdCwAA1C6yXeZYu3btnDlzFi5cKITo3bt3v379Vq9e3bdv\nXyHEkCFDZsyYsX79+qioKLkOBwAAahHZznCcP3/e29vb/LF5YS69Xl8x2qVLl6ysLLmOBQAA\nahfZCkf79u337t1r/njfvn1CiMrLkx85cqR9+/ZyHQsAANQusl1SmTJlyuuvv56dnd2iRYv4\n+PiXXnppwYIFzZs379at265duz788MOIiAi5jgUAd9i7d298fHxVowcOHHj88cetmQfAHWQr\nHJMmTbp58+aqVauOHDkya9asiIiIWbNmjR071jw6cuTImTNnynUsALjD5cuXi4qKqhq9fft2\nSUmJNfMAuINshcPOzm7mzJmVW0V0dPSIESPOnj3r5eXl5eVV1fu6AYDlXnjhhRdeeKGq0bCw\nMGuGAXA3BRfj0mg0zzzzzDPPPKPcIQAAQK0g202jAAAAVaFwAAAAxVE4AACA4igcAABAcRQO\nAACgOAoHAABQHIUDAAAojsIBAAAUR+EAAACKo3AAAADFUTgAAIDiKBwAAEBxCr55GwAAlpMk\nSQgRGBjYoIGlv7M++uijsWPHyhEKD43CAQCwaebCERoaOmzYMEvmmT59elZWlkyh8NAoHACA\nWqBz586DBg2yZIamTZvKFQY1wD0cAABAcbZ4hiMvL+/48eNVjWZnZ7u4uFgzDwAAsJAtFo6E\nhISFCxdWNXr9+nVPT09r5gGgKEmSMjMzs7Ky8vLyTCaTTqfz8PDQ6/UajUbtaABkY4uFY+bM\nmTNnzqxqNCwszJphACgqISEhKioqNTX1ju0+Pj7h4eHBwcGqpAIgO1ssHADqibi4uNDQ0ICA\ngDlz5nh6erq5uUmSVFhYmJGRsXHjRqPRWF5ePmrUKLVjApABhQOAalasWBESEhIbG1v56omH\nh4evr6/RaJwxY8by5cspHEDdwKtUAKgmIyNj4MCBVd2rMWjQoPT0dCtHAqAQCgcA1fj4+CQl\nJZWWlt49ZDKZEhMTfX19rZ8KgBK4pAJANfPnzw8KCvLz8zMajV5eXq6urkKIoqKitLS0pKSk\nlJSU5ORktTMCkAeFA4Bq/P39d+zYER0dHRERYTKZKrZrtdrAwMClS5caDAYV4wGQEYUDgJoM\nBoPBYCguLs7JycnNzRVCuLu763Q6Jyenh5rn4MGDmzZtqmr08OHDbdq0sTQrAAtQOACoTJIk\nR0dHvV6v1+tLS0t/+OGHI0eOeHt7P/HEE9Wf5Pz584cPH65qtKCgwHy9BoBaKBwAVFNSUhIe\nHr527drS0lKj0bh8+fL+/fsfOnTIPDp69OiYmBgHB4fqTDV8+PDhw4dXNcqCgYDqeJUKANVE\nRUUtX758yJAh06dP//7775977rnc3NytW7eePHly5cqVmzZtWrZsmdoZAciDMxwAVBMXFzd7\n9uz3339fCNG/f/+BAwd++eWXAQEBQgi9Xn/u3Ln169e/9dZbascEIAPOcABQzfnz559++mnz\nxz4+PkKIyvdt+Pr6njp1Sp1kAORG4QCgmtatW//222/mj11cXDZu3Ni5c+eK0czMTHd3d5Wi\nAZAZl1TuIT8/Xwhh+btja7XarVu39ujRQ6ZcQF0THBy8ePFiSZL8/f2ffvrpESNGmLdfvXp1\n27ZtS5YsCQkJUTchALlQOO7hypUrQojIyEidTmfJPOPGjcvOzpYpFFAHvf3224WFhQsWLNi5\nc+fu3bsrtvfs2TMjI+NPf/pTZGSkeukAyInCUaXBgwd36tTJkhkmTJggVxigTnrkkUc+++yz\n5cuXX7x4sfL2hQsXPv744926dbPwLCMA20HhAKAyR0fHtm3bVt5ScW0FQJ0hc+GQJCkzMzMr\nKysvL89kMul0Og8PD8tvhgAAALWanIUjISEhKioqNTX1ju0+Pj7h4eHBwcEyHgsAANQishWO\nuLi40NDQgICAOXPmeHp6urm5SZJUWFiYkZGxceNGo9FYXl4+atQouQ4HAABqEdkKx4oVK0JC\nQmJjYytfPfHw8PD19TUajTNmzFi+fDmFAwCA+km2hb8yMjIGDhxY1b0agwYNSk9Pl+tYAACg\ndpGtcPj4+CQlJZWWlt49ZDKZEhMTfX195ToWAACoXWS7pDJ//vygoCA/Pz+j0ejl5eXq6iqE\nKCoqSktLS0pKSklJSU5OlutYAACgdpGtcPj7++/YsSM6OjoiIsJkMlVs12q1gYGBS5cuNRgM\nch0LAADULnK+LNZgMBgMhuLi4pycnNzcXCGEu7u7TqdzcnKS8SgAgPtbtGjRpk2bLJwkNzdX\nkiRZ8gBCiYW/srOzKxb+KikpkSSJhb8AwJp++uknNze34cOHWzLJhx9+mJWVJVckgIW/AKAO\n8vHxmThxoiUzfP311xQOyIiFvwAAgOJsceGv8+fP//TTT1WNnj17tnnz5jIkBgAA1iJb4cjI\nyJg6dep9Fv5as2ZNNaf65ptvFixYUNXo9evXn3zyyRokBAAAapGtcJgX/ho9erS9vf0dQw+7\n8Ne0adOmTZtW1WhYWFjNUwIAADWw8BcAAFAcC38BAADFsfAXAABQnMwLfwkhnJyc9Hq9Xq8X\nQty4ceP111+fN29ely5dZD8QAFQ4evTo9u3bqxo9fvy4TqezZh4Ad5C/cFR2+/bttWvXjhs3\njsIBQFHp6ek7duyoajQnJ8fR0dGaeQDcQbbC0aZNm7s3lpeXCyFGjhzp4OAghDh//rxchwOA\nykaPHj169OiqRnl1G6A62QrHmDFjoqOjnZycxowZ06DB/01bUlKyevXqvn37tm7dWq4DAQCA\nWke2whEVFRUUFBQSEnL06NG4uLjOnTsLIS5fvrx69erp06f3799frgMBAIBax07GuQwGQ2pq\nateuXZ966qmPP/7YfD0FAABAzsIhhHB2do6JiUlISIiMjPT39+edBgEAgJC9cJi99NJLx48f\nd3R07NWrlxLzAwCA2kWpl8W6u7tv2bIlPj7+xIkTHh4eCh0FAADUCgquw6HRaF555RXl5gcA\nALWFIpdUAAAAKqNwAAAAxVE4AACA4igcAABAcRQOAACgOAoHAABQHIUDAAAojsIBAAAUR+EA\nAACKo3AAAADFUTgAAIDiFHwvFQCoDkmSMjMzs7Ky8vLyTCaTTqfz8PDQ6/UajUbtaABkQ+EA\noKaEhISoqKjU1NQ7tvv4+ISHhwcHB6uSCoDsKBwAVBMXFxcaGhoQEDBnzhxPT083NzdJkgoL\nCzMyMjZu3Gg0GsvLy0eNGqV2TAAyoHAAUM2KFStCQkJiY2MrXz3x8PDw9fU1Go0zZsxYvnw5\nhQOoG7hpFIBqMjIyBg4cWNW9GoMGDUpPT7dyJAAKscUzHGfPnv3Pf/4jSdI9R0+ePOnu7m7l\nSACU4OPjk5SUNHr0aHt7+zuGTCZTYmKir6+vKsEAyM4WC8e2bduio6OrGs3Pzy8tLbVmHgAK\nmT9/flBQkJ+fn9Fo9PLycnV1FUIUFRWlpaUlJSWlpKQkJyernRGAPGyxcEyePHny5MlVjYaF\nhVkzDADl+Pv779ixIzo6OiIiwmQyVWzXarWBgYFLly41GAwqxgMgI1ssHHVGaWnpN998Y+FF\naI1G89JLL+n1erlSATbFYDAYDIbi4uKcnJzc3FwhhLu7u06nc3Jyeqh5Tpw48d1331U1evz4\n8datW1uaFYAFKBwKunnz5vbt20+cOGHJJL///ntBQcH7778vVyrABjk5Oen1ekuK9aFDhzZu\n3FjV6NmzZxs2bFjjyQFYjsKhrLCwsMWLF1syQ1BQUFX3zwKoEBoaGhoaWtUol2IhhLh+/frx\n48fvU0yrycvL64knnpAlUr1C4QAA1AtnzpzJzMw8ePCgJZMUFBT069dv8+bNcqWqPygcAFTT\nt2/fB+6zb98+KyRBPfHss89+//33lswwe/ZsloepGRb+AqCa8ePH5+fn79+/v6CgwKUKamcE\nIA/OcABQTVhY2JAhQ9q2bTt+/PhZs2apHQeAgjjDAUBNLVu27Nmzp9opACiOMxwAVLZs2bKm\nTZuqnQKAsigcAFTm5+endgQAiuOSCgAAUByFAwAAKI7CAQAAFEfhAAAAiqNwAAAAxVE4AACA\n4igcAABAcazDAQA2pKSk5MaNGxZOUlpaKksYQEYUDlsnSdKtW7eKioosnKdx48YNGzaUJRIA\n5XTp0uXs2bOWz3Pz5k3LJwFkROGwdceOHdu6deuKFSssnGfw4MHbtm2TJRIA5Vy+fDk6Orp/\n//6WTOLv719SUiJTIkAeFA5bV1ZW5u3tvWnTJksm+fTTTw8cOCBXJACK6tChQ/fu3S2ZoUED\nntthc/ihrAUaNWrUvn17S2ZwdXWVKwwAADXAq1QAAIDiKBwAAEBxXFIBUC/0OHtWbNyodooH\ne7G0tPWBA8Ky17UOLSl5tLDQwq/XkJfnXlZm4SQdjx4dKYQmKUlotTWexM5kGilEx6NHLQzz\nUllZp7w8CyfxzshonpNTK36W5DRypOVzUDgA1AuhBw6IlBS1UzzY8hs3Gn/6qVi92pJJlly9\nqr1+XUyaZMkk04uLy8rKLJxkQElJLyG0r79uySRaIT4X4pENG4Rlt89/eOtWg99+s/Areqm4\nuKys7MqoUZZMIoTQarVOTk4WTmI9Nlg4JEnKzMzMysrKy8szmUw6nc7Dw0Ov12s0GnkPdB9N\nysuFZatW2BcXuwqhvXrVwnlchXC8dcvCSVwkqUlZmYWTnD169PThw90ef9ySSYQQzZs3//77\n76353YT8bO8OYus8b0wZMyYmJkbGCRXyuKtrTEzMiy++aMkknVu2bNeu3cGDBy2ZZPjzz//0\n009XCwstmWTVihXTpk0rvXjRkhfOlJaWNmvYcMX770+ZMsWSMB7Ozs8888z3339vySQDevZM\nT0+Pjo62ZJJjx4599dVXRZY9trWOnIUjISEhKioqNTX1ju0+Pj7h4eHBwcEyHqsqnQ4e/CUz\nUzRrZskkgUIUCiF69LAwTIEQYvlysXy5JZNkCCHy8y38ilaZ/8/y1YTOnhVubpZOAnVJktoJ\n/octPG8AD8XR0XHixImWzPDtt99+9dVXcuWpLWQrHHFxcaGhoQEBAXPmzPH09HRzc5MkqbCw\nMCMjY+PGjUajsby8fJTF56Ae6NEzZ35+5JFee/ZYMsnu3btnzZr1zTffeHh4WDJPjx49xo0b\n98Ybb1gyib+/v06nW7t2rSWTTJkyJTU1dY9lD8svv/wyefLk9957z8K/O+3s7AwGA+sEQNjM\n84YsJEn697//XVxcbOE8paWlZWVlskQCbIpsT/orVqwICQmJjY2t/NvIw8PD19fXaDTOmDFj\n+fLl1XziyMzM3LVrV1WjJ0+efOXmTbFq1T1HW588uVajST18+GHzV3bs1KnDQqz99deW+fmW\nzHNYiOY5OfaWhfm5tNTt+vVVlk2y6+rV0+XlFk6ye8+ew0L4v/WWJZOY9ejRo2nTppbMUFhY\n2L179w4dOlgySX5+/vXr19u1a2fJJCUlJRcuXLBwmSYhxNGjR318fOzsLHrhmEajefHFFx99\n9FELw1iNNZ83WrZsWdVobm5ufHy8yWR6qPB3yM/PX7p0qSUzVIiJiSm07GT7zZs3L168uKqK\n58lqOn/+fGlpqYWTmJccXL16tSU/2+Zvzf79+y18f4bS0tILFy5Y+BXl5+ffvHnTwkl++OGH\na9eu+fn5WTKJEKKoqGjs2LGPPPKIJZNoNJqxY8e2atXKwjAPPpAk0/lVZ2fnjz/+OCQk5J6j\nycnJY8aMuXLlSnWmWr169XvvvVfV6JUrV07culXVc8fN27dfFeJny34oTSbTxYsX3d3dLfxT\nPi8vz9XV1cL/QoqKiuzt7S28t+j69eslJSXNLLsuU1ZWdunSJXd3d0smEULk5u1W7uIAACAA\nSURBVOY2b97cwjMchYWFDg4OjRs3tmSS4uLi0tJSC1dFu337dlFR0X1+mVWHJEm5ubktWrTQ\nWnAnvxBCq9V+8cUX/fr1s2QSa7Lm80a/fv2+/vrre47++OOPEyZMsLBw8LxxTzxv3FP9fN6Q\nrXA8++yzrq6uX3/9tb29/R1DJpMpLCzsjz/++PHHH2U5FoC6gecNoP6Q7ZLK/Pnzg4KC/Pz8\njEajl5eXuf0VFRWlpaUlJSWlpKQkJyfLdSwAdQPPG0D9IdsZDiHEnj17oqOjt27dWvnMpFar\nDQwM/Otf/2owGOQ6EIA6g+cNoJ6Qs3CYFRcX5+Tk5ObmCiHc3d11Ol1tWtsEgBp43gDqPPkL\nBwAAwB148zYAAKC4urb4UnJy8uLFi728vNQOIoQQx44d0+v1Fr4ESxaXLl0qKCjo3Lmz2kGE\nEOLQoUNeXl6NGjVSO4jIycm5ceOGhYt5yEKSpCNHjmzdurVFixZqZ6mPeN64J5437onnjRqr\na2c4Dh069Ntvv6md4v8cO3Ys37Klw+Ry/vz59PR0tVMI8f//F1Jk2VvDyOXcuXOZmZlqpxBC\niJKSksOHD//xxx9qB6mneN64J5437onnjZqT6pbPPvusc+fOaqf4Py4uLps2bVI7hSRJ0uLF\ni5955hm1U0iSJJlfifDjjz+qHUSSJGn27NmBgYFqp5AkSTL/gjl+/LjaQeopnjfuieeNe+J5\no8bq2hkOAABggygcAABAcRQOAACgOAoHAABQHIUDAAAojsIBAAAUR+EAAACKo3AAAADFaRcs\nWKB2Bjk1bdq0VatW3bt3VzuIEEI4ODgMHjy4SZMmagcRzs7O7dq18/b2VjuI0Gg0Dg4OgYGB\njo6OamcRTk5OnTp1euKJJ9QOIho1amR+Q3Z7e3u1s9RHPG/cE88b98TzRo3xbrEAAEBxXFIB\nAACKo3AAAADFUTgAAIDiKBwAAEBxFA4AAKA4CgcAAFAchQMAACiOwgEAABRH4QAAAIqjcAAA\nAMVROAAAgOIaqB0AAFAtt2/fzs7OrrxFq9U+9thjauUBHopNn+HYvn27wWBwdnZ++umn4+Pj\na7BnaWnpkiVLvLy8nJycevbsuWrVqprNb1MUfVjKy8vXrFnj4+PTuHHjDh06TJ8+/fLlywp+\nMfJR+qelwty5c9u0aSNzeiijmj8VN2/efPvttzt16uTo6NipU6eFCxeWlJTcvZuF33rLw+zb\nt+/x/9WjRw9Vkggh/vjjj+DgYJ1O5+7uPn78+EuXLtUgieVhbt26dfZeapDH8oelvLz8s88+\ne/LJJx955JHOnTsvWrTonj9I1glTzSc0q5Js1Y8//mhvbx8UFBQbGzt27FghREJCwsPu+eqr\nrzZs2HDevHn//Oc/p0+frtVqly1b9rDz2xSlH5ZPP/1UCBEWFvbPf/7z3XffbdKkSe/evcvK\nyqz05dWU0g9L5U/XaDStW7dW9uuBHKr/U/Haa685OjpGRkYmJSXNmTNHo9HMnDnz7tks+dbL\nEmbVqlUODg6bKtm6dasqSc6dO9emTZu+ffuuXr06IiLCxcXlueeee9gksoTZu3fvPX+1hYaG\nWjmJJElLly4VQkyZMmXDhg3h4eH29vZTp059qBgyhqnOE5qV2W7hGDp0qLe39+3btyVJKi8v\nHzx4sLe3d3l5efX3zMzMFEJUfogjIyNbtmxZUlLyUPPbFKUfltatWwcFBVUMJSUlCSG2bdum\n+BdmGaUfFrMrV660a9euSZMmFI5aoZo/FTdu3LCzs4uMjKzY8sorr7i5uVXe0/JvvSxh5s6d\n27Vr15oFkDfJX//6165du968edM8tG7duu7du2dlZVk/zKVLlzb9r08++cTOzu6bb76xchJJ\nkjp37vznP/+5YujNN9985JFHavAHm+VhqvOEZn02WjiuXbum1WoXLVpUsWXdunVCiIyMjOrv\n+fXXXwshjh8/XjF06NAhIcSePXuqP79NUfphKSgoEEJ89tlnFUMXL16846fWBin9sFRsCQsL\n69mz56RJkygctq/6PxVnz57t16/fzz//XLFl/vz5zs7OlX9PWPitlyvMyJEjhw4dKklSaWlp\nDWLIlaSsrMzNzc38tFBaWmoymVQMc8eeZWVlzz333IwZM1RJ0q5du9dee61i6B//+IeDg0NF\nLbNmmOo8oVmfjd7DkZOTYzKZPD09K7Z4eXkJIbKysqq/Z4sWLYQQZ86cqRj6/fffhRDZ2dnV\nn9+mKP2wNG7cOC0tbcyYMRVDe/bsEUK0b99eiS9HLko/LOZ/fvvttxs2bIiLi2vQgFuta4Hq\n/1S0bdt29+7dTz/9tMlkKiws3LVrV1xcXHBwsFarNe9g+bderjCnTp3Ky8vz9fVt2LChTqeb\nNGlSUVGR9ZNcvHixoKDA2dl58ODBzs7Orq6uY8eONf+5Yv0wd+wZHR1dUFDw/vvvq5Jk3Lhx\n8fHxycnJV69e3bdv30cffTRq1KhGjRpZP8wDn9BUYaOFIzc3VwjRrFmzii1ubm5CiLy8vOrv\n6efn16lTp5kzZ+7ZsycvL2/Lli0zZ840D1V/fpui9MPi4ODQpUuXJk2amD9l//79EydO9PLy\nCgwMVPYLs4zSD4v5fydMmBAVFdW5c2fFvx7IoQb/jW/atMnNzW3AgAEtWrT48MMPzRtl+dbL\nEkaSpFOnTqWmpo4ePTo5OfmNN96Ij49/4YUXysvLrZwkJydHCDFlyhSdTrd+/fp3331369at\ngYGBD5VErjCVXbhw4Z133lm+fLm9vb0qSSIiIgYNGhQUFNS0adNnn322TZs2X3755UMlkSvM\n/Z/Q1GKjheNukiQJIUwmU/X3bNSo0aZNm5o2bdqvXz93d/eQkJDw8HDxv9/IGsxvUxR6WIqK\niqZOnWowGNq3b79169Za9ze9vA+LJEmvvvqqj4/P66+/rnRyKOeBPxUDBgzYv3//F198kZOT\n079/f/NlC4W+9TUIY34FxH//+9+5c+cGBAS8/fbbn3zyyf79+3fu3GnlJOZXrg0dOjQmJubF\nF1+cNm3aF198cfDgQQuT1CxM5dG33npr4MCBAwYMsDBGzZJIkjR79uzdu3cvW7Zs9+7dq1at\nunDhQkhIyB0hrRPmoX79WY2N/iJxd3cXQlQ+W1hYWCiE0Ol0D7Vn165df/nllwsXLly+fLlL\nly5Hjx4VQrRq1ar689sUpR8W857bt28PCwsrKSn54IMPXnvttYf9W8H6lH5Y4uPjf/jhh59/\n/vnq1atCiJKSkvLy8suXLzds2PCRRx5R+qtDzdTgv/FmzZr17t27d+/erVu3HjJkyA8//HDx\n4kVZvvWyhHn++edHjRpVeZ+hQ4cKIVJSUv70pz9ZM4l556CgoIp9zAEeKolcYZ5//nnz0OnT\np+Pj43ft2lX9APImadq06dKlS+Pj419++WUhRL9+/Z544olnn3122LBhwcHBVg7z/PPP3/95\nXhU2eoZDp9PZ2dmlpaVVbMnIyBBCeHh4VH/P27dv7969Oycnp02bNl5eXg0aNPjpp5/s7Oy6\ndOlS/fltitIPixDi3//+95AhQ3x8fDIyMqZOnWr7bUMo/7CcOHHixo0b3t7erq6urq6uq1ev\nzsnJcXV15YSHLav+T0VSUlKXLl3MlcKsY8eOQojLly/L9a2XJUxWVtZ3331369atiiE7Ozsh\nhLOzs5WTmH9pVV5hwvxHfMXVWGuGqdjyySefdOrUyWAwPFQGGZOYb5jo1q1bxVD37t2FEKdO\nnbJ+mPs/z6vG6repVtcLL7zQo0ePivufhw8fXtULHava02QyPfrooxUv8rx586a3t3fFP6s/\nv01R9GEpKyvz8PAIDAys8W3nalH0YTl16tSuSl588cXmzZvv2rUrLS3NKl8caqiaPxXmu/cT\nExMrtphXozlx4oSM33rLw5h/A61atapiKDY2Vghx7NgxKyeRJKl3797PPfdcxWeZh44cOfJQ\nSeQKI0lSSUmJi4vLwoULHzaAjElSUlKEECtXrqwYSk5OFkJs2bLF+mHu/+tPLbZbOMwrn7zy\nyivJyckzZswQQmzYsME89MknnwwcOPD06dMP3HPx4sVCiDlz5sTExDz33HPOzs6//PLLAz/L\nlin6sJiX0HnllVeW/K+UlBRVvtjqU/qnpbI33niDl8XWCtX8qSgvLx80aFDTpk0XLlyYmJj4\n1ltvOTo6jh49+u4JLfnWyxJmxIgRjo6Of//7381DjRo1evXVV1VJsmXLFjs7uxdeeCE+Pv5v\nf/tbw4YNQ0JC1HpYJEnasWOHEOKnn36qQQa5kpSXl48YMaJRo0bz5s1LTEx85513XFxcnnnm\nmRq8hlmWh6WaT2jWZLuFQ5Kk77//vm/fvk2aNOnRo8f69esrtk+fPl387yuMq9qzrKxs0aJF\nHh4erq6ugYGBhw4dqs78Nk65hyUmJuaep8G++OILq311Nab0T0sFCkctUs2fioKCgtdff71t\n27aNGjXq2rXrwoULb926dfdsFn7rLQ9TXFw8Z84cDw+PRo0aeXt7L126tGarAMvysGzZsqVP\nnz5NmjTp0qXLu+++W+OlQWQJ8+abbzZu3Ni8UlaNWZ7k5s2bCxcufOKJJxo1atSxY8eZM2cW\nFRWpFaaaT2jWpJEkyeLLMgAAAPdjozeNAgCAuoTCAQAAFEfhAAAAiqNwAAAAxVE4AACA4igc\nAABAcRQOAACgOAoHAABQHIUDAAAojsIBAAAUR+EAAACKo3AAAADFUTgAAIDiKBwAAEBxFA4A\nAKA4CgcAAFAchQMAACiOwgEAABRH4QAAAIqjcAAAAMVROAAAgOIoHAAAQHEUDgAAoDgKBwAA\nUByFAwAAKI7CAQAAFEfhAAAAiqNwAAAAxVE4AACA4igcAABAcRQOAACgOAoHAEBO48aN02g0\nGo0mPT1d7SywIRQOAACguAZqBwAA1Cnt2rXr3r27EKJRo0ZqZ4EN0UiSpHYGAABQx3FJBfLo\n37+/+art1atXIyMjW7ZsGRsbq3YoAIo4cODAsGHD2rZt6+joqNfrX3755ePHj1eMjhgxwvxs\ncPbs2YqN165dmzJlSufOnVu2bGk0Gi9evNiuXTuNRtOrVy/zDr6+vhqNplGjRvn5+UajsWXL\nlh07dpw4ceKlS5eys7ODg4Nbt2796KOPvvjii5mZmZXDbNu2zd/fv02bNg4ODm3bth02bNje\nvXut8jDgIUmAHPr162f+iZo9e7b5g5iYGLVDAZDfli1b7v5V0qBBgz179ph3GD58uHnjmTNn\nzFsuXbrk6elZef9OnTo1a9ZMCPH000+b9/Hx8RFCaLXaDh06VN6zZ8+eHh4elbe0b9/++vXr\n5s+KiYm5O4xWq/3xxx+t/sDgATjDAZl98MEHzs7OPj4+TZs2VTsLAPnNmzdPCGFnZ/fRRx9t\n3779nXfeadiwYVlZ2ZtvvlnVp7z33nsnTpwQQrz00kt79uxZs2ZNXl5eYWHh3XuaTKZbt269\n9957EydO1Gg0Qoj//ve/+fn5c+fOnTt3rouLixDi9OnT5nMYkiSZ/8JxcXFZvHhxUlLS5MmT\nzZOsWrVKkS8eFuCmUcjsz3/+c0xMjKOjo9pBAMivtLQ0LS1NCKHT6YYPH96qVas//elPTZo0\nOXbsmFarNZlMWq32jk8pKSn5+OOPhRAeHh6JiYn29vbPPvuss7PziBEj7nmIr7/++umnnxZC\n/PHHH99//70Q4r333ps+fboQolGjRpGRkUKIU6dOCSHy8/PNewYFBb322mvmD1atWmUymU6e\nPKnYY4AaonBAZn//+99pG0Bd1aBBgzZt2mRlZV24cMHDw6NXr17PP//84MGDp06denfVMDt1\n6lRJSYkQIjAw0N7e3rzxpZdeatSo0a1bt+7YWaPRmF/hIoRo166d+YOePXvesaW8vFwI0aJF\ni++++06SpBMnTsTExBw/fnzPnj0mk6liB9gULqlAZq1bt1Y7AgClaDSapKSkJ598UghhMpn2\n798fERHRs2fP9u3bb9q06Z6fcubMGfMHLVq0qNhoZ2en0+nu3tnOzq5Bgzv/Eq6oKXfbsmVL\nu3btnnzyyb/85S/Lly/PzMy0s+P3mo3iGwOZ8V87ULf17NkzJSXl8OHDERER5js9hRDnzp0L\nDg6u/LKUChU9Iycnp2JjWVlZ5X/WzJkzZ4KDg8+dO9eqVauoqKhDhw5dunTJwcHBwmmhEH43\nAACq65dffpkyZcrUqVOvXbsWGRl57Nix06dPDxo0SAhRVlZ2+PDhuz+lY8eO5g82bdpUXFxs\n/njdunV3X095WHv27DFfrHnzzTdnz57dvXv348eP37x508JpoRDu4QAAVJejo+Mnn3wihNi2\nbdu8efM6dOiQm5tb8XoTvV5/96e4urr++c9//uabb/Lz85977rmwsLAzZ858+OGHsoQxf7B2\n7VqdTldSUrJo0SLLp4VCKBwAgOry9PScMGHCF198cfr06YkTJ1YeCgoK8vLyuudnLV68eM+e\nPZcuXTp06NChQ4eEEC4uLrdv375x44YlYfr169esWbPCwsITJ0688sor4v9f3qOwsLCwsFCS\nJPMLa2EjuKQCAKgujUazcuXKr776asCAAY899ljDhg0fffRRPz+/Dz74IDExsapbuDp37nzk\nyJFRo0Y99thjzZs3HzZs2NGjRx999FELw7Rs2fLf//53//79nZycOnXqNG3atEOHDvXp00cI\ncebMmcTERAvnh7x4LxUAgLWZTCYXF5fi4uJhw4Z9++23aseBNXCGAwCgoNu3b7u6ujZo0KBx\n48b//e9/hRBlZWXz588330BqPiGB+oAzHAAAZUVFRc2dO9f88WOPPXbt2rXLly8LIZ5++ukf\nf/yRF7LWExQOAIDivv/++5UrV6akpOTk5DRr1uzxxx8fO3bsX/7yl0aNGqkdDVZC4QAAAIrj\nHg4AAKA4CgcAAFAchQMAACiOwgEAABRH4QAAAIqjcAAAAMVROAAAgOIoHAAAQHEUDgAAoLgG\nageAym7cuPHee++Vlpbef7dz58798MMPjRs3fuCE06ZNmz59ukzpANi0ixcvDhw48MaNG9Xc\nv2nTpnv37q3OMwnqHgpHfff7778vXLhw2LBhDRs2vM9uBw8eLCgoeOedd+4/W2xs7LFjx2QN\nCMB25eXl/frrr8uWLatOh8jNzf373/++ePFiZ2fn6kzepEmTSZMmabVai2PCJlA4IIQQa9as\nadas2X12GDt27MaNGydOnHj/eX766SdZcwGoBUJCQtzc3B64286dO4UQ33zzTXXaye3bt48f\nP/7888936NBBhoiwARQOAIA1mN8rdN26dX5+fg/c+fz584899hhvL1qXcNMoAABQHIUDAAAo\njsIBAAAUJ/M9HJIkZWZmZmVl5eXlmUwmnU7n4eGh1+s1Go28BwIAALWInIUjISEhKioqNTX1\nju0+Pj7h4eHBwcEyHgsAANQishWOuLi40NDQgICAOXPmeHp6urm5SZJUWFiYkZGxceNGo9FY\nXl4+atQouQ4HAABqEdkKx4oVK0JCQmJjYytfPfHw8PD19TUajTNmzFi+fDmFAwCA+km2m0Yz\nMjIGDhxY1b0agwYNSk9Pl+tYAACgdpGtcPj4+CQlJd3zLTlMJlNiYqKvr69cxwIAALWLbJdU\n5s+fHxQU5OfnZzQavby8XF1dhRBFRUVpaWlJSUkpKSnJyclyHQsAANQushUOf3//HTt2REdH\nR0REmEymiu1arTYwMHDp0qUGg0GuYwEAgNpFzpfFGgwGg8FQXFyck5OTm5srhHB3d9fpdE5O\nTjIeBQAA1DryrzTq5OSk1+v79Olz69atzZs3r1+//u6VOQAAQL0izxmOrKysHj16xMTEBAQE\nCCGKiopeeOGF/fv3V+wwYcKETz/9VKvVynI4AHUJKxQD9YE8hcNkMuXl5ZWUlJj/OXfu3GPH\njsXGxg4dOlSj0Xz77beTJ0/u2rXrm2++KcvhANQZrFAM1BOKvHnb5s2bw8PDQ0NDXV1dXVxc\nxo0bN3369LVr1ypxLAC1V1xc3NixY1u3bh0fH3/06NFz58798ccfR48e3bBhQ8eOHY1G44YN\nG9TOCEAeMr95mxCirKwsPz+/W7dulTc+9dRTH330UTVn+PDDDyMjI6savXXrVt++fbdv325R\nSgA2gBWKgfpD/sLRoEGDJ5988vjx44MHD67Y+Ntvv7Vo0aKaM4wcObJVq1ZVja5cudLFxcXS\nlABsQEZGxtSpU++zQvGaNWusHAmAQuQsHKNGjerQoUPHjh0dHR0XLFgQEBDg5eV169atdevW\nLVmyZPr06dWcp1WrViNHjqxqdOvWrTLlBaAy8wrFo0ePtre3v2OIFYqBOkaewtGqVaudO3ee\nOnXq1KlTp0+fLi0ttbe3//XXX728vHbs2DFx4sSRI0e+/fbbshwLQJ3BCsVA/SFP4WjYsOGA\nAQMGDBhQsUWSpPLyciGEj49Penp6586dZTkQgLqEFYqB+kP+ezjMNBqNedWNxx57TKFDwAZd\nunQpJyfn/ffff+Ce5tcmWCESbJxcKxQnJyff56VwFy5c6NOnT1RUlKVxAdSUUoUD9VN6evqF\nCxd27Nhx/90OHDjg6uo6ceJE66SCjTOZTPb29nq9Xq/Xl5aWbtq0KSkpycvLKyAgoEGD6j5H\nNWnSxHxF5p5SUlJSUlJkygugJigckFnr1q3/85//3H+fLl26SJJknTywZSUlJbNnz/7yyy9N\nJtPo0aNXr149bty49evXm0d79+69devWpk2bVmcq85mSqkbDwsLkSQygpmQrHH379n3gPvv2\n7ZPrcADqgCVLlnz22WdTpkxp0aLFihUrevfunZ2dvXfv3m7duu3evXvMmDGLFi3iOghQN8hW\nOMaPH/+Pf/zj5MmTXbp06dChg1zTAqjD1q5dO2fOnIULFwohevfu3a9fv9WrV5v/ehkyZMiM\nGTPWr19P4QDqBtkKR1hY2JAhQ9q2bTt+/PhZs2bJNS2AOuz8+fPe3t7mj318fIQQer2+YrRL\nly5ZWVnqJIPazK9zXLVqlZubW3X2d3R0nDx58t0LusB2yHkPR8uWLXv27CnjhADqtvbt2+/d\nu9f8Dm3mS65Hjx6tuBXjyJEj7du3VzMf1HPx4kUhxObNm5s0afLAncvKylJSUgYOHOjp6al8\nNNSQzDeNLlu2rJp3eAHAlClTXn/99ezs7BYtWsTHx7/00ksLFixo3rx5t27ddu3a9eGHH0ZE\nRKidEeow31e+cuXKgQMHPnDnS5cuPfroo9yKbuNkLhx+fn7yTgigDps0adLNmzdXrVp15MiR\nWbNmRUREzJo1a+zYsebRkSNHzpw5U92EAOTCy2IBqMbOzm7mzJmVW0V0dPSIESPOnj3r5eXl\n5eVV1fu6Aah1KBwAbIhGo3nmmWeeeeYZtYMAkJmd2gEAAEDdR+EAAACKo3AAAADFcQ9HXTZ4\n8ODMzMz773P79u2K/wUAQCEUjrps3759YWFhTz755H32OXLkyOeff379+nWrpQIA1EMUjjpu\n8ODBgYGB99khKSnp888/t1oeAED9ROEAAPw/kiTt3bu3mpdZz5w5o3Qe1BkUDgDA/3Ps2LF+\n/fo91KdcvXq1mm+xhvqMV6kAAP6fsrIyIURxcbFUDV9//XXFpwD3R+EAAACKo3AAAADFUTgA\nAIDiKBwAAEBxFA4AAKA4CgcAAFAchQMAACiOwgEAABRH4QAAAIqjcAAAAMVROAAAgOIoHAAA\nQHEUDgAAoDgKBwAAUFwDtQMAqO8kScrMzMzKysrLyzOZTDqdzsPDQ6/XazQataMBkA2FA4Ca\nEhISoqKiUlNT79ju4+MTHh4eHBysSioAsqNwAFBNXFxcaGhoQEDAnDlzPD093dzcJEkqLCzM\nyMjYuHGj0WgsLy8fNWqU2jEByIDCAUA1K1asCAkJiY2NrXz1xMPDw9fX12g0zpgxY/ny5RQO\noG7gplEAqsnIyBg4cGBV92oMGjQoPT3dypEAKITCAUA1Pj4+SUlJpaWldw+ZTKbExERfX1/r\npwKgBJkvqXC3OYDqmz9/flBQkJ+fn9Fo9PLycnV1FUIUFRWlpaUlJSWlpKQkJyernRGAPOQs\nHNxtDuCh+Pv779ixIzo6OiIiwmQyVWzXarWBgYFLly41GAwqxgMgI9kKB3ebA6gBg8FgMBiK\ni4tzcnJyc3OFEO7u7jqdzsnJ6aHmOXfu3MGDB6saPXv2rJubm6VZAVhAtsLB3eYAaub8+fNt\n2rTR6/UdOnTYsWPH5s2bmzRp8vTTTz/UDRz/+te/li1bVtVofn5+586d5QgLoIZkKxwZGRlT\np069z93ma9asketYAOqGS5cujRw58tq1a4cOHbp06VJQUFDlsxQhISFffvllgwbVepp64403\n3njjjapGw8LCZIgLwAKyvUqFu80BPKzZs2cfO3bszTffFEJMmzYtMzMzKSnpypUrly5dWrly\n5VdffRUVFaV2RgDykO0MB3ebA3hYycnJ06dPHzt2bHl5+Xfffbdo0aLhw4ebhyZPnnz+/PmE\nhITw8HB1QwKQhWyFg7vNATwsrVbbtm1bIUR5eXlZWZmHh0fl0S5dumRlZakUDYDM5HxZrFx3\nmwOoJ/r06RMTEzNmzBgHBweDwbB58+Zhw4aZhyRJ4lIsUJfIv/BXdnZ2xcJfJSUlkiSx8BeA\ne4qOju7bt2+3bt1effXVESNGTJ069caNG0FBQbdu3UpISNizZ8/mzZvVzghAHiz8BRVIknTj\nxo2ioqL772Zvb8/psbqtXbt2Bw4c+OijjxYtWlRQUCCESExMTExMFEL06dNn8+bNQUFBamcE\nIA8W/oIKzp07N3PmzJkzZ95/Nzs7u99///3xxx+3TiqowsPDIzo6+v3337948WJOTs7ly5eb\nN2/eqlWr5s2bqx0NgJxY+AsqKC8vDwgIePfdd++zz9WrVwcMGHDt2jWrq+doYAAAHZVJREFU\npYKKtFqtTqfT6XRqBwGgFFtc+GvDhg1ffvllVaO//fZb+/btaxIRtqRZs2bdu3e/zw6FhYVW\nCwMAUJpshcO88Nfo0aPt7e3vGHrYhb86deo0aNCgqkaLioqaNm1a86AAAMDqbHHhr27dunXr\n1q2q0fT0dHkSAwAAa2HhLwAAoDgW/gIAAIqTeeEvIYSTk5Ner9fr9bLPDAAAainZ3i0WAACg\nKhQOAACgONkuqfTt2/eB++zbt0+uwwEAgFpEtjMc48ePz8/P379/f0FBgUsV5DoWAACoXWQ7\nwxEWFjZkyJC2bduOHz9+1qxZck2LeyouLr548eIDd5MkyQphAAB4IDlfpdKyZcuePXvKOCGq\n8vLLL2/ZsqU6ex4/fjwwMFDpPAAA3J/ML4tdtmwZ645bwY0bN954440Hvttqhw4dbt26ZZ1I\nAADch8yFw8/PT94JURVXV1fexA4AKly9erWoqKg6e9rb27MipfXJv/AXAADWdOPGDSFEnz59\nqrm/nZ1dWlpap06dlAyFO1E4AAC1m/na8ZIlS5577rkH7nzz5s1nn332ypUryufC/6BwAADq\ngg4dOnTv3v2Bu12/ft0KYXA3VhoFAACKo3AAAADFUTgAAIDiKBwAAEBxFA4AAKA4CgcAAFAc\nhQMAACiOdTgAqEySpMzMzKysrLy8PJPJpNPpPDw89Hq9RqNROxoA2VA4AKgpISEhKioqNTX1\nju0+Pj7h4eHBwcGqpAIgOwoHANXExcWFhoYGBATMmTPH09PTzc1NkqTCwsKMjIyNGzcajcby\n8vJRo0apHbPWu3r16pIlS0pLS6uzc05OjtJ5UD9ROACoZsWKFSEhIbGxsZWvnnh4ePj6+hqN\nxhkzZixfvpzCYbnU1NSFCxcOHDiwOlepzIXj+vXrjRs3Vj4a6hEKBwDVZGRkTJ06tarfgoMG\nDVqzZo2VI9VJkiQJIb7//nutVvvAndeuXTtu3DjFM6H+4VUqAFTj4+OTlJR0z1P9JpMpMTHR\n19fX+qkAKIEzHABUM3/+/KCgID8/P6PR6OXl5erqKoQoKipKS0tLSkpKSUlJTk5WOyMAeVA4\nAKjG399/x44d0dHRERERJpOpYrtWqw0MDFy6dKnBYKj+bJcvXzZfO7jb7du3GzZsaGlcABag\ncABQk8FgMBgMxcXFOTk5ubm5Qgh3d3edTufk5PRQ8yxcuHD+/Pn32cHb29uioAAsQ+EAoD4n\nJye9Xq/X64UQN27ceP311+fNm9elS5fqzzBt2rSAgICqRiMjI5s0aSJDUAA1ReEAYFtu375t\nfqHEQxUOZ2fn7t27VzXq5uYmRzQANUfhAKCaNm3a3L2xvLxcCDFy5EgHBwchxPnz560dC4AC\nKBwAVDNmzJjo6GgnJ6cxY8Y0aPB/T0clJSWrV6/u27dv69at1Y0HQEYUDgCqiYqKCgoKCgkJ\nOXr0aFxcXOfOnYUQly9fXr169fTp0/v37692QACyYeEvAGoyGAypqaldu3Z96qmnPv74Y/P1\nFAB1D4UDgMqcnZ1jYmISEhIiIyP9/f2zsrLUTgRAfhQOADbhpZdeOn78uKOjY69evdTOAkB+\n3MMBwFa4u7tv2bIlPj7+xIkTHh4eascBICcKBwAbotFoXnnlFbVTAJAfl1QAAIDiKBwAAEBx\nXFKBjSorKxNCTJo06YFv4tWpU6dPPvnEKqEAADVE4YCNunbtmhDC3d3dvBhUVU6dOrV27VoK\nBwDYOAoHbNrLL788YsSI++yQnJy8bds2q+UBANQM93AAAADFUTgAAIDiZL6kIklSZmZmVlZW\nXl6eyWTS6XQeHh56vV6j0ch7IAAAUIvIWTgSEhKioqJSU1Pv2O7j4xMeHh4cHCzjsQAAQC0i\nW+GIi4sLDQ0NCAiYM2eOp6enm5ubJEmFhYUZGRkbN240Go3l5eWjRo2S63AAAKAWka1wrFix\nIiQkJDY2tvLVEw8PD19fX6PROGPGjOXLl1M4AACon2S7aTQjI2PgwIFV3asxaNCg9PR0uY4F\nAABqF9kKh4+PT1JSUmlp6d1DJpMpMTHR19dXrmMBAIDaRbZLKvPnzw8KCvLz8zMajV5eXq6u\nrkKIoqKitLS0pKSklJSU5ORkuY4FAABqF9kKh7+//44dO6KjoyMiIkwmU8V2rVYbGBi4dOlS\ng8Eg17EAAEDtIufLYg0Gg8FgKC4uzsnJyc3NFUK4u7vrdLoHvvnWHfbs2ZOQkFDV6IEDB9q1\na2dhVAAAYE3yv5eKk5OTXq/v0KHDzp07N2/e7Ozs3KtXL29v7+rPcPXq1aKioqpGb9++fc87\nRQAAgM2Sp3BkZWX16NEjJiYmICBACFFUVPTCCy/s37+/YocJEyZ8+umnWq22OrMFBQUFBQVV\nNRoWFmZ5YABAffbxxx/rdLrq7Ong4DB79uyHPVWPu8lTOEwmU15eXklJifmfc+fOPXbsWGxs\n7NChQzUazbfffjt58uSuXbu++eabshyuDrt169Zvv/32/7V351FRlf8fwB+YYRFkEIFiFMlE\nxAMIkigdQSbXJFA6EYIe11JxO6Un99QorU4ueUo9WXlyQ0vBDBMz01yysgIXNkEdRKbAUZbB\nAVlmub8/5vyIr8mdy3Cfe4fx/fqPez99ns/zcB0+zdx5LsMw7GFarVav1wtTEgCALWloaCCE\n5Obmcmk4GIY5c+bM2LFjo6Oj6Zdm46g8nj4rK2v16tUzZsww/Thz5szi4uK9e/ei4TBry5Yt\na9as4RLp4uJCuxgAAFu1bNmy1j9SLAwGg1QqNfs/gcAF/w2HXq+/f//+c8891/ZgeHj4p59+\nyvtYtqepqUmhUBw9epQ9zN/fH+9wAABAF8J/wyGVSgcNGpSfnz9+/PjWg0VFRU899RTvY9kk\nBwcH0y4mLPD0XQAA6Fp422mUEJKSkhIcHJyQkNCtW7e0tLSCggJCSFNT05dffrlp06bJkyfz\nOBYAAAB0Ify8w9GrV68zZ84olUqlUllaWqrT6RwcHAoKCkJCQk6fPj137tykpCSOtyYAwJOG\nYZibN2+qVCq1Wm0wGORyuZ+fX0BAAN7JA7Al/DQcjo6Oo0aNGjVqVOsRhmGMRiMhJCwsrLi4\nODAwkJeBAMDGHDhwYOPGjXl5eY8cDwsLW7169aRJk0SpCgB4R+VbKoQQOzs7064bffr0oTQE\nAHR1+/btmzFjRmxs7PLly4ODgz09PRmGqampKSkpycjISE5ONhqNKSkpYpcJADyg1XAAAJi1\nbdu26dOn79mzp+2nJ35+foMHD05OTl6yZMnWrVvRcADYBj5vGgUA6JCSkpLRo0e3d6/GmDFj\niouLBS4JACjBOxwAIJqwsLDMzMzJkyc7ODg8cspgMBw6dGjw4MGiFGb9/vnnn6VLl7Z9NDeL\nqqoq2vUAmIWGAwBEs3bt2vj4+IiIiOTk5JCQENMONLW1tdevX8/MzLx27Vp2drbYNVqpwsLC\nw4cPz549m0twRUUFIcRoNHJ8oBUADWg4AEA048aNO3369ObNm9etW9f2f9YlEklcXNyWLVti\nYmJELM/KSaXSzz//nEvk9u3b2z5NE0AUaDgAQEwxMTExMTH19fWVlZV3794lhPj4+Mjl8o4+\nnPPIkSM7d+5s72xRUVH//v07WysAdAIaDgAQk16v/+mnn4qLi/v16xcXFyeV/vuilJeX9+ef\nf3L81MDX13fIkCHtnVWr1a6urjyUCwCWQsMBAKLRaDQvvfTS77//bvoxJCTkhx9+8PX1Nf14\n6tSpZcuWcWw4IiMjIyMj2zurVqs7Xy0AdAa+FgsAolm3bl1BQUFmZua9e/cyMzMrKioSExPx\nJGQAm4SGAwBEc/z48ZUrVyYmJnp7eycmJh47diwnJ+ezzz4Tuy4A4B8aDgAQjVqtHjBgQOuP\nUVFR8+fPf/fdd6urq0WsCgBoQMMBAKLx9/c/efJk2yPr1693cnKaPn266emPAGAzcNMoAIjm\njTfemDNnjlqtjo+PnzJlipubm4eHx1dffRUXF5eQkGDaBwwAbAMaDujatFptS0vLypUrzUYq\nFIrY2FgBSgLuXnvtNZ1Ot2HDhuPHjysUioEDBxJCXnzxxe+//z41NVWlUoldIADwBg0HdG0l\nJSU6nS43N5c9TKlU5ubmouGwNvb29vPnz58/f35NTU3bfTJiY2NLS0svXbp069YtEcsDAB6h\n4YCujWEYQshPP/3EHrZ27dpLly4JUhFYomfPno8ckUql0dHR0dHRotQDALzDTaMAAABAHRoO\nAAAAoA4NBwAAAFCHezgE0tLSkp2dbXbP5uvXrzc0NAhTEgAAgGDQcAjk559/TkxM7NGjB3uY\nVqt1d3cXpiQAAADBoOEQiMFgcHFxqampYQ8bMWJEUVGRMCUBAAAIBg0HAADA45m+eJ+SkuLs\n7Mwl3snJKSsrKyAggHJdXRIaDgAAgMczPdNHoVC88MILXOIXLFhQVlaGhuOx0HAAAACwiYqK\nmjt3LpfIRYsW0S6m68LXYgEAAIA6NBwAAABAHRoOAAAAoA4NBwAAAFCHhgMAAACoQ8MBAAAA\n1KHhAAAAAOqwDwcAgFXIz89PSkrS6XRcghsbG80+DBLAqqDhgCeCVqtVq9UZGRlmI6Oionr1\n6iVASQCPuH379p07dz755BMuwSdPnjx69CjtkgB4hIYDngiXL18uLCxcuXIle1hlZeXy5cvT\n0tIEKQrgUY6Ojhx3tKyurkbDAV0LGg54IjAM06NHD6VSyR42ZswY06MTAACAX2g4OothmJ07\ndz548IA9rLi4GB+4AgDYvPr6+traWi6REolEJpPRrsd6oOHoLI1Gs2DBgqCgoG7durGEVVRU\ntLS0CFYVAAAIT6fTvfLKK9zjz58/HxMTQ68eq4KGo7MYhiGEfP3116GhoSxhaWlp7777rlBF\nAQCAOBYtWjRz5kwukQqFQqPRUC7HiqDhAAAA4E3v3r2HDBnCJVIikdAuxqpg4y8AAACgDu9w\nAPzLYDDU1taWlpayh0mlUj8/P2FKAgCwDWg4AP5VWFh47ty57du3m408d+6cQqEQoCQAANuA\nhoPNuXPnbty4wR7T0NBACDEYDIJUBHQZDIaIiIhDhw6xh4WEhNTX1wtTEgCAbeC54WAY5ubN\nmyqVSq1WGwwGuVzu5+cXEBBgZ2fH70DCmD9/flVVFfv3pE27a9y+fTs8PFyouoCibt269evX\njz3G3h43P/HJxl432vrrr7+mTJnCcTe5hw8fPnz4kHZJYD2amprWrVu3bds2LsH29vZbt24N\nCgqiXRU9fDYcBw4c2LhxY15e3iPHw8LCVq9ePWnSJB7HEgbDMBs2bEhNTWWJUSqV/fv3x/aU\nTxSGYW7dupWbm8se1r1798DAQGFK6rps73Wjrdu3b6vV6s2bN3MJzsrK+uGHH2iXBNZDp9O5\nurpy/ErLtm3bCgoK0HAQQsi+fftmzJgRGxu7fPny4OBgT09PhmFqampKSkoyMjKSk5ONRmNK\nSgpfwwGIqLGxcfHixWbD7Ozs6urq3NzcBCipi+qKrxstLS2//vorx09R8/PzuT8epby8HA3H\nk2bkyJEbNmzgErl79+6GhgaOe5hKpVIrfOWxM+1b1XlDhw4NCgras2fPY98FXbJkyW+//fbH\nH39wSXXz5s2zZ8+2d3bv3r3TGhvnzZv32LNqtfr06dNmJ1VWVqZSqbgUExAQEBkZyRKg1Wqz\nsrJiYmLYv7aQl5eXl5c3depU9uFOnTpVV1eXlJTEHpaRkeHu7j5u3Dj2sPT09NDQUPYdycrL\nyy9cuJCQkMB+dV68eLG8vHzKlCnsI2ZlZRFCEhIS2MMOHjzo5+cXHR3NEtPVF7aqqurkyZNh\nYWFSKVtb39zcrNfrn3nmGfYR6+rqHB0dvby82MMIIcOGDfPw8GCL4PbHTxhCvm68U1HR3m/2\nwYMHeXl5HF8M6+rqKioquES2GjFiBJewO3fulJeXcwxWqVRlZWUcgysqKpRKZXR0NJdPqdRq\n9Y0bN55//nkHBwezwdXV1UVFRREREexbLZtoNJr8/Pzw8PDu3bubDdZqtVevXh00aFCPHj3M\nBjc2Nubk5AQFBXl6epoN1ul0ly5dGjBgwNNPP202mGGYixcv9u/fXy6Xmw0mhPzyyy99+/bt\n06cPx2A/Pz+z//xNLl682KG/1z4+Pi4uLhyDw8PDzSzd559zH7o9vDUcMpls+/bt06dPf+zZ\n7OzsKVOm1NXVcUm1a9euDz/8sL2zdXV1hU1N7V0ojY2NVVVVZocwfQJi9pN4g8FgZ2fHHsYw\njMFgkEgk7P+STWHsf3tMhTEMY3Y3GC6FEUL0ej3HwsyGcSwMC/tIYQIvLCHEy8vLzEu/uSfY\nCUnI141jzs7Dhw9/7Nn79+/n5ORwfDE0Go06nc7JyUncYIZhWlpauAc3Nzc7OzuLG0wIaWpq\nohfs5OTE8b4fesHNzc2Ojo7cgx0cHDjeE0Yv2M7OLiIiwtvbmy3o8GEuqcwMxFfDMWLECA8P\njyNHjvy3KTYYDLNmzbpz58758+d5GQsAbANeNwCeHLzdw7F27dr4+PiIiIjk5OSQkBDTm7q1\ntbXXr1/PzMy8du1adnY2X2MBgG3A6wbAk4O3dzgIIRcuXNi8efOJEyfa3k4lkUji4uLeeuut\nJ+eBeADAHV43AJ4QfDYcJvX19ZWVlXfv3iWE+Pj4yOVyLvcHAcCTDK8bADaP/4YDAAAA4BHY\nMBEAAACow7NUBHLlypXU1NSuu/25RqP5+++/Q0JCxC7EQmq1WqvV9u/fX+xCLFReXh4ZGZmW\nliZ2IbYpOzv7gw8+EPLyLioq8vHx6dmzpzDDNTU1FRQURERECDMcIaSsrEwqlfr6+gozHMMw\nf/31V3h4OJe9Q3hx7949jUYzYMAAYYYjhFy7dq1fv36CbedVX19fW1t74sQJHnPiHQ6BFBQU\nXLlyRewqLFdZWVlUVCR2FZZTqVQlJSViV2G50tLSX3/9VewqbFZOTo7Al3dRUVFHdw/rDI1G\nc/nyZSE/QFcqlWVlZYIN19zcfPXqVa1WK9iIwr+k5OXl3b9/X7Dh7t27d+HCBZ6TMiCI48eP\nu7q6il2F5Xbu3BkYGCh2FZZbs2bNmDFjxK7CcjNnzpw5c6bYVdgs4S/v0NDQTz75RLDhTH85\n9Hq9YCOmpKTMmzdPsOFM+z2atosVRlpamkKhEGw4hmGeeuqpQ4cOCTbc4cOHvb29+c2JdzgA\nAACAOjQcAAAAQB0aDgAAAKAODQcAAABQh4YDAAAAqEPDAQAAANSh4QAAAADq0HAAAAAAdRJs\nliwMd3d3T0/P4cOHi12Ihdzd3Xv16jVkyBCxC7GQm5ubv79/cHCw2IVYyNXVddCgQf7+/mIX\nYpuEv7ydnZ0VCoW3t7cww7m7u8tkMoVCIcxwhBAXF5fw8PC+ffsKM5yzs7NEIomPjxdsa3OZ\nTPbss88KuR2+k5PTuHHjZDKZMMO5u7t7e3tHRkbymBNPiwUAAADq8JEKAAAAUIeGAwAAAKhD\nwwEAAADUoeEAAAAA6tBwAAAAAHVoOAAAAIA6NBwAAABAHRoOAAAAoA4NBwAAAFCHhgMAAACo\nQ8MBAAAA1EnFLgBsTUtLS0VFRdsjEomkT58+YtXzpMH6g1m4SEAUeIfDEqdOnYqJiZHJZJGR\nkenp6Wbjd+/eHR0dzT1JR/N3FNX6L168+Oz/Gjp0qBXWz3KqS6x/e6cEWH8rx+PyEkJWrFjh\n6+vbmfy86/wE2S8SG5ggIeTOnTuTJk2Sy+U+Pj6vv/56VVWVxfl518kJNjU1lT1O6xxFn2C7\nGOig8+fPOzg4xMfH79mzZ+rUqYSQAwcOsMSr1erAwMCoqCiOSTqa39rq/+KLL5ycnI62ceLE\nCWur37KpdYn6aa+/leNxeU3Z7OzsevfubXF+3vEyQZaLxDYmWF5e7uvrGx0dvWvXrnXr1vXo\n0WPkyJGW5edd5yf4yy+/PPav+YwZMyzILyQ0HB02ceLE0NDQlpYWhmGMRuP48eNDQ0ONRuN/\nI3NychQKhZOTEyHkkX8PLEm457fO+lesWBEUFMRXtZTqt2xqXaJ+2utv5XhZXpO6urq+ffu6\nubm1bThoXx5m8TJBlovENib41ltvBQUFNTY2mn7cv3//kCFDVCpVh/JT0vkJVlVVHf1fO3bs\nsLe3//bbbzuUX3hoODpGq9VKJJL333+/9cj+/fsJISUlJf8NvnHjxqZNmzZt2jRw4MC2lwtL\nkg7lt8L6GYZJSkqaOHEiwzA6nY6Xmnmv3+KpWX/9DOX1t3J8La/JrFmzhg0blpqa2tpw0L48\nzOJrgu1dJLYxQb1e7+np+fHHHzMMo9PpDAaDZflp4PcSNdHr9SNHjlyyZElH8wsP93B0TGVl\npcFgCA4Obj0SEhJCCFGpVP8NDggIWLp06dKlS/39/Tkm6VB+K6yfEKJUKtVq9eDBgx0dHeVy\neWpqam1tLS/F81W/xVOz/voJ5fW3cnwtLyHku+++++abb/bt2yeV/ntnPe3Lwyy+JtjeRWIb\nE7x37151dbVMJhs/frxMJvPw8Jg6dWp1dXVH89PA4yXaavPmzdXV1R999FFH8wsPDUfH3L17\nlxDSs2fP1iOenp6EELVazUsSXvJbNjQvSRiGUSqVeXl5kydPzs7OXrhwYXp6+oQJE4xGo/XU\nb8P5aa+/leNredVq9Zw5czZu3BgYGEgjv8V4KYDlIrGNCVZWVhJCFi1aJJfLDx48uH79+hMn\nTsTFxdnMBNv6559/3nvvva1btzo4ONDIzy98LbazGIYhhBgMBkpJeMlv2dAWJDEajTt37gwJ\nCTG11bGxsb6+vrNmzTpz5szYsWN5Kbi9oWkk73L5hV9/K2fB8jIMM3v27LCwsAULFtDIzy8L\nCmC5SJydnTufn18WFKDRaAghEydO3L17t+lI7969X331VZuZYFurVq0aPXr0qFGjKOXnFxqO\njvHx8SGEtH2PuqamhhAil8t5ScJLfsuG5iWJRCJJSUlpGzxx4kRCyLVr13j5g9cl1kfE/LTX\n38rxsrzp6ek///zzpUuXHjx4QAhpbm42Go0ajcbR0ZH2r88sXgpguUgSEhI6n78zeJmgl5cX\nISQ+Pr71iOnit5kJtiotLU1PTz979iyl/LzDRyodI5fL7e3tr1+/3nqkpKSEEOLn58dLEl7y\nWzY0L0lUKtXx48ebmppaT9nb2xNCZDJZ54tnHxr5CSG019/K8bK8hYWFDx8+DA0N9fDw8PDw\n2LVrV2VlpYeHx4IFC2j/+szipQCWi8Q2JtirVy9CSHNzc+sRnU5HCHFzc7ONCbbasWPHgAED\nYmJiKOXnHRqOjunevXtcXNyRI0daPxTPyMgIDQ0NCAjgJQkv+UWsv6GhYcKECab7ok2ysrII\nIZGRkdZTvw3np73+Vo6X5Z07d+7ZNl5++WUvL6+zZ8+uXLmS9q/PLF4KYLlIbGOCXl5ew4cP\nP3jwoOnTBFMSQsiwYcNsY4ImLS0tX3311bRp0+zs7Gjkp0LQ78TYBNO2KtOmTcvOzl6yZAkh\n5JtvvjGd2rFjx+jRo0tLSx/5T+Li4h67u9Rjk7Cc6hL1v/rqq926dXvnnXcOHTq0atUqZ2fn\n2bNnW1v9lk2tS9RPe/2tHL/LyzDMwoUL/7vxF73LwyxeJshykdjGBI8dO2Zvbz9hwoT09PS3\n337b0dFx+vTpZvMLg69L9PTp04SQ33//nXt+0aHhsMSPP/4YHR3t5uY2dOhQUx9t8uabbxJC\n8vPzH4l/7OXSXhL2U9Zff319/fLly/38/JydnUNDQ7ds2aLX662wfpZTXWL92zslwPpbOR6X\nl/lPw8GSXzCdnyD7RWIDE2QY5tixY1FRUW5ubgMHDly/fn3bHUdsY4KLFy92dXU1bfDFMb/o\n7Jj/f9MJAAAAgBLcwwEAAADUoeEAAAAA6tBwAAAAAHVoOAAAAIA6NBwAAABAHRoOAAAAoA4N\nBwAAAFCHhgMAAACoQ8MBAAAA1KHhAAAAAOrQcAAAAAB1aDgAAACAOjQcAAAAQB0aDgAAAKAO\nDQcAAABQh4YDAAAAqEPDAQAAANSh4QAAAADq0HAAAAAAdWg4AAAAgDo0HAAAAEAdGg4AAACg\nDg0HAAAAUPd/ichTd8WYelsAAAAASUVORK5CYII=",
"text/plain": [
"Plot with title “sigma”"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot.hists(samps, my.par=c(2,2), n.hists=4, priors=priors, mai=c(0.5, 0.5, 0.25, 0.2))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The prior distribution here is very different from the posterior. These data are highly informative for the parameters of interest and are very unlikely to be influenced much by the prior distribution (although you can always change the priors to check this). However, notice that $Y_0$ (the initial condition) is truncated by the prior. This is a fairly strong prior, because we know something about the initial optical density that is typical for the esperimental set up with the density of innoculum used and with a properly calibrated set-up."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Visualizing the joint posterior of parameters \n",
"\n",
"It's often useful to also look at the joint distbution of all of your parameters together. Of course, if you have a high dimensional posterior, rendering a 2-D representation can be difficult. Instead, the standard is to examine the pair-wise posterior distribution, for instance as follows (using the `s1` data frame we created above):"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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ly5cuDAgeTkZHt0kuP0bly7jQ+OIxeJ4cCAw2EGDBhw6NChBx54wPDjkCFDtm3b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\ngg==",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ipairs(s1[,2:5], ztransf = function(x){x[x<1] <- 1; log2(x)})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see, estimates of $r$ and $K$ are highly correlated -- not surprising given the interplay between them in the logistic growth function. This correlation is an important feature of the system, and we use the full posterior distribution that includes this correlation when we want to build the corresponding posterior distribution of the behavior of the logistic function.\n",
"\n",
"#### The posterior distribution of the mean function\n",
"\n",
"The final step is to check how well we are fitting the data. To do this we usually examine the posterior distribution of the mean function of our system, in this case the distribution of the logistic solution and compare this to the data. To do this, for each of our posterior samples (or a thinned subset), we plug the parameters for the $i^{\\mathrm th}$ sample $\\theta_i$ into our function of interest, and evaluate the function as a desired set of $x$'s. For instance, for logistic growth, we'll evaluate \n",
"$$\n",
"\\mu(t) = \\frac{K_iY_{0,i}}{Y_{0,i}+(K_i-Y_{0,i})\\exp{(-r_it)}}\n",
"$$\n",
"for the $i^{\\mathrm th}$ set of parameters for a sequence of times, $t$. This we obtain points describing the curve $\\mu_i(t)$ for each set of parameters. Here is one way to do this:"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [],
"source": [
"my.logistic<-function(t, Y0, K, r){\n",
" return(K*Y0/(Y0+(K-Y0)*exp(-r*t)))\n",
"}\n",
"\n",
"ts<-seq(0, 40, length=100)\n",
"ss<-seq(1, dim(samps)[1], by=10)\n",
"my.curves<-matrix(NA, nrow=length(ss), ncol=length(ts))\n",
"\n",
"for(i in 1:length(ss)){\n",
" my.curves[i,]<-my.logistic(t=ts, Y0=samps$Y0[i], K=samps$K[i], r=samps$r[i])\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now plot all of these curves:"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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z5bVFQUjkNjcCCE0F9kZGTklVdOv/22327fzXEVVVWjBz/VnJQhiuBidKBb6B/o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ub9wJ9IXHjq/RE2pBHAAAP8O3L6nU1dXp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\nsXH2XH36Ik3+T2vWryI7OwBA5/t54dDQ0Pj227y8vPbVzfv06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8VOXDG7zG1w2Si3mprH0lITRIrKzuwQufzeerXI7OJI8YuKl0w/ObxS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",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(ts, my.curves[1,], col=1, type=\"l\", ylim=c(0.09, 0.36), \n",
" ylab=\"predicted OD\", xlab=\"time (days)\")\n",
"for(i in 2:length(ss)) lines(ts, my.curves[i,], col=i)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Then we can summarize this posterior using the `apply` function to find the mean and the (for simplicity) quantile based 95% CI:"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [],
"source": [
"m.log<-apply(my.curves, 2, mean)\n",
"l.log<-apply(my.curves, 2, quantile, probs=0.025)\n",
"u.log<-apply(my.curves, 2, quantile, probs=0.975)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For comparison, here is how to find the 95% HPD Interval across time, using the `HPDinterval` function from the `coda` package:"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [],
"source": [
"hpd.log<-NULL\n",
"for(i in 1:length(ts)){\n",
" hpd.log<-cbind(hpd.log, as.numeric(HPDinterval(mcmc(my.curves[,i]))))\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And plot these together with the data (in this case the HPD and quantile based intervals are indistinguishable):"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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+XHq8HhcMhksgpXdwqFwmAw2O323RzVeg0NDVKpdGxsLB6Po2dIkkSVFCiKslqt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7Ua/B6EQuHKyorP52MYRqFQJJNJyt6h6Hk2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\n/lUAgLPcmTzCM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"text/plain": [
"Plot with title “LB-AB isolate, T=12C”"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"my.ylim<-c(0.09, 0.45)\n",
"my.title<-\"LB-AB isolate, T=12C\"\n",
"\n",
"plot(d2$DAY-1, d2$OD, xlim=c(0,max(Temps)), ylim=my.ylim,\n",
" pch=(mycol+20),\n",
" xlab=\"time (days)\", ylab=\"\",\n",
" main=my.title,\n",
" col=\"grey\", cex=1.5)\n",
"lines(ts, m.log, col=1, lwd=2)\n",
"lines(ts, l.log, col=2, lwd=2, lty=2)\n",
"lines(ts, u.log, col=2, lwd=2, lty=2)\n",
"\n",
"lines(ts, hpd.log[1,], col=3, lwd=2, lty=3)\n",
"lines(ts, hpd.log[2,], col=3, lwd=2, lty=3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that this only shows the uncertainty in the *mean function* -- the assumed model with log normal noise says that the observations simply have this mean. The fit is attributing the majority of the observed noise to process error rather than parameter uncertainty."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Readings and Resources <a id='Readings'></a>\n",
"\n",
"* Motulsky, Harvey, and Arthur Christopoulos. Fitting models to biological data using linear and nonlinear regression: a practical guide to curve fitting. OUP USA, 2004.\n",
"* Johnson, J. B. & Omland, K. S. 2004 Model selection in ecology and evolution. Trends Ecol. Evol. 19, 101–108.\n",
"* The [NCEAS non-linear modelling working group](https://groups.nceas.ucsb.edu/non-linear-modeling/projects/OrangeTree)\n",
"* [Mixed-Effects Models in S and S-PLUS](https://link.springer.com/book/10.1007/b98882)\n",
"* Bolker, B. Ecological models and data in R. (Princeton University Press, 2008). "
]
}
],
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"kernelspec": {
"display_name": "R",
"language": "R",
"name": "ir"
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"codemirror_mode": "r",
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"equation": "Ctrl-E",
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"title_cell": "Contents",
"title_sidebar": "Contents",
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"left": "10px",
"top": "150px",
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