{ "metadata": { "name": "", "signature": "sha256:35c27d2f649f82beff2f40adc51fc75156a6a79f0ca04cc748450d23d3caa352" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Difficult to sample probability distributions arise very naturally in the [Bayesian approach to Statistics](https://en.wikipedia.org/wiki/Bayesian_inference). Here we use Bayes' rule in the following form:\n", "$$ \\mathbb P(\\theta | D ) = \\frac{\\mathbb P(D | \\theta) \\mathbb P(\\theta)}{\\mathbb P(D)} $$\n", "where $\\theta$ represents our statistical model (usual a parameterised model, hence the symbol $\\theta$) and $D$ represents our data. We typically don't have access to $\\mathbb P(D)$, the probability of the data. $\\mathbb P(\\theta)$ is our _prior_ belief about the model. $\\mathbb P(D | \\theta)$ is the _likelihood_, the probability of seeing the data given a choice of $\\theta$. Hence we apply Bayes' rule in the form\n", "$$ \\mathbb P(\\theta | D ) \\propto \\mathbb P(D | \\theta) \\mathbb P(\\theta) $$\n", "Notice that we get an un-normalised probability distribution, which is fortunately exactly what we've been dealing with in our MCMC methods.\n", "\n", "What question do we want to answer? Back in my undergrad days, my basic statistics course spent some time on [maximum-likelihood estimation](https://en.wikipedia.org/wiki/Maximum_likelihood). Once we have fixed our model, we find the value of $\\theta$ which makes the likelihood $\\mathbb P(D|\\theta)$ most likely. In the Bayesian setting, if we fix a uniform (\"uniformative\") prior, then this is the same as asking which value of $\\theta$ maximises the posterior probability $\\mathbb P(\\theta|D)$. However, it would be more in keeping with Bayesian philosophy to actually think about the _distribution_ $\\mathbb P(\\theta|D)$. To think about why, consider these two possibilities:\n", "\n", " - The distribution is very sharply peaked around the maximum likelihood.\n", " - The distribution is very flat with the maximum likelihood tying to one exteme of where the distribution is supported.\n", " \n", "In the 1st case, the maximum likelihood seems a very reasonable single fact to report; in the second, it might be fairer to say that the data has told us rather little, and we actually have rather little knowledge of $\\theta$.\n", "\n", "There are, of course, also situations where the prior becomes important (to pick one example, dealing with many bits of data, and using previous data to inform our prior when dealing with new data).\n", "\n", "For complicated models, $\\mathbb P(D | \\theta) \\mathbb P(\\theta)$ becomes hard to sample from, and this is where MCMC methods become useful: we draw many samples from the distribution $\\mathbb P(\\theta|D)$ and use these to give a numerical approximation to the distribution." ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "The plan" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can easily find tutorials and resources online. Let me pick out:\n", "\n", " - [Pythonic Perambulations](https://jakevdp.github.io/) and in particular the four linked articles: [Part I](http://jakevdp.github.io/blog/2014/03/11/frequentism-and-bayesianism-a-practical-intro/), [Part II](http://jakevdp.github.io/blog/2014/06/06/frequentism-and-bayesianism-2-when-results-differ/), [Part III](http://jakevdp.github.io/blog/2014/06/12/frequentism-and-bayesianism-3-confidence-credibility/), [Part IV](https://jakevdp.github.io/blog/2014/06/14/frequentism-and-bayesianism-4-bayesian-in-python/) dealing with Bayesian ideas in Python.\n", " - [EMCEE](http://dan.iel.fm/emcee/current/) which I'm going to use below: [Regression Example](http://dan.iel.fm/emcee/current/user/line/)\n", " \n", "In fact, I have issues with the Pythonic Perambulations presentation. So, actually, let's attack simple regression first." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mathematical model is that $(x_i)$ are given points, and $y_i = a + bx_i + e_i$ where $e_i \\sim N(0,\\sigma^2)$ represents the uncertainty in our measurements. Note the asymmetry here: each $x_i$ is known with certainty, and all the uncertainty is in $y_i$. Much more on this can be read about here: http://arxiv.org/abs/1008.4686\n", "\n", "So\n", "$$ f(y | a, b, \\sigma^2) = \\prod_i (2\\pi\\sigma^2)^{-1/2} \\exp\\Big( -\\frac{(y_i - a - bx_i)^2}{2\\sigma^2} \\Big). $$\n", "\n", "That just leaves the issue of finding the prior. Let's defer this..." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def sample_data(a, b, sigma, n):\n", " x = np.sort( np.random.random(size = n) * 50 )\n", " y = a + b*x + np.random.normal(scale = sigma, size = n)\n", " return x,y\n", "\n", "x, y = sample_data(5, 3, 8, 20)\n", "_ = plt.scatter(x,y)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEACAYAAAC9Gb03AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 42 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We define a Python function which is the log of the likelihood, and then evaluate at the known \"actual\" parameters. Then we'll use the `scipy` package to find the maximal likelihood (although, in this case, we of course know a closed form solution for this)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def log_likelihood(theta, x, y):\n", " a, b, sigma = theta\n", " return - np.sum((y - a - b*x)**2) / (2 * sigma**2) - x.size * np.log(sigma*sigma) * 0.5\n", "\n", "log_likelihood((5, 3, 8), x, y)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 103, "text": [ "-47.495561772643228" ] } ], "prompt_number": 103 }, { "cell_type": "code", "collapsed": false, "input": [ "import scipy.optimize as op\n", "nll = lambda *args: -log_likelihood(*args) # Minimise the negative to get the maximum!\n", "result = op.minimize(nll, [5, 3, 8], args=(x, y))\n", "a_est, b_est, sigma_est = result[\"x\"]\n", "print(a_est, b_est, sigma_est, \"-->\", log_likelihood((a_est, b_est, sigma_est), x, y) )" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "3.51146082401 3.06088920588 6.08486037495 --> -46.1160736448\n" ] } ], "prompt_number": 104 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll now introduce a prior: at present, I'm using a flat prior on $a$ and $b$ but the Jeffrey's prior on $\\sigma$." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def log_prior(theta):\n", " a, b, sigma = theta\n", " return - np.log(abs(sigma))\n", "\n", "def log_prob(theta, x, y):\n", " return log_prior(theta) + log_likelihood(theta, x, y)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 105 }, { "cell_type": "code", "collapsed": false, "input": [ "import emcee\n", "ndim, nwalkers = 3, 50\n", "sampler = emcee.EnsembleSampler(nwalkers, ndim, log_prob, args=[x, y])\n", "\n", "starting_guesses = np.random.normal(0, 0.1, (nwalkers, ndim)) + [a_est, b_est, sigma_est]\n", "sampler.run_mcmc(starting_guesses, 2000)\n", "emcee_trace = sampler.chain[:, 1000:, :].reshape(-1, ndim).T" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 106 }, { "cell_type": "markdown", "metadata": {}, "source": [ "I'll use the [Triangle Plot](https://github.com/dfm/triangle.py) package to show the marginals." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import triangle\n", "figure = triangle.corner(emcee_trace.T, labels=[\"$a$\", \"$b$\", \"$\\sigma$\"], truths=[5, 3, 8])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAgQAAAIECAYAAABmAjaWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 107 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The historgrams are the marginal distributions, and the three density plots are the correlations. The lines mark the \"real\" parameters.\n", "\n", " - One can of course cheat and re-run the above: sometimes it works out very closely, but I have left here a \"difficult\" case." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What the [Pythonic Perambulations](https://jakevdp.github.io/blog/2014/06/14/frequentism-and-bayesianism-4-bayesian-in-python/) post now does is the following piece of code.\n", "\n", "The `numpy` pattern is as follows:\n", " - `alpha, beta` are set to the list of samples of our posterior\n", " - `alpha[:, None]` makes a new view of alpha of shape ? by 1\n", " - Then the broadcasting rules mean that `yfit` is of shape ? by 20 (20 because that's the size of xfit).\n", " - Then `.mean(0)` and `.std(0)` compute the (sample) mean and standard deviation of the first axis." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_MCMC_model(ax, xdata, ydata, trace):\n", " \"\"\"Plot the linear model and 2sigma contours\"\"\"\n", " ax.plot(xdata, ydata, 'ok')\n", "\n", " alpha, beta = trace[:2]\n", " xfit = np.linspace(0, 50, 20)\n", " yfit = alpha[:, None] + beta[:, None] * xfit\n", " mu = yfit.mean(0)\n", " sig = 2 * yfit.std(0)\n", "\n", " ax.plot(xfit, mu, '-k')\n", " ax.fill_between(xfit, mu - sig, mu + sig, color='lightgray')\n", "\n", " ax.set_xlabel('x')\n", " ax.set_ylabel('y')\n", " \n", "fig, axes = plt.subplots(figsize=(8,6))\n", "axes.set_xlim([0,50])\n", "plot_MCMC_model(axes, x, y, emcee_trace)\n", "\n", "alpha, beta = emcee_trace[:2]\n", "print(\"Line:\", alpha.mean(), beta.mean())" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Line: 3.67671802535 3.05446620054\n" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAfgAAAF/CAYAAAClndsfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nvIiIiAP9f4a7QnMzJMkOAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 108 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This code has the following effect:\n", "\n", " - Look at all the samples $(a_i, b_i)$ form the posterior (discard the $\\sigma_i$).\n", " - For each $x$ value compute $a_i + x*b_i$ and then from these samples compute the sample mean and standard deviation\n", " - Now plot the mean, and +/- one standard deviation\n", " \n", "For a linear model, we can compute this exactly. Fix a value of $x$.\n", "\n", "$$ \\mu = \\frac1n \\sum_{i=1}^n a_i + b_ix = \\overline a + \\overline b x $$\n", "\n", "\\begin{align*} \\sigma^2 &= \\frac1n \\sum_{i=1}^n (a_i + b_ix)^2 - \\mu^2\n", "= \\Big(\\frac1n \\sum_i a_i^2 - \\overline a^2\\Big) + \\Big(\\frac1n \\sum_i b_i^2 - \\overline b^2\\Big)x^2\n", "+ 2x \\Big( \\frac1n\\sum_i a_ib_i - \\overline a\\overline b \\Big) \\\\\n", "&= \\sigma_a^2 + \\sigma_b^2x^2 + 2x \\Big( \\frac1n\\sum_i a_ib_i - \\overline a\\overline b \\Big)\n", "\\end{align*}\n", "\n", "So the line is just obtained by taking the mean of $(a_i)$ and $(b_i)$." ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Simple Hierarchical model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here I'm following [Jordan's lecture course](http://www.cs.berkeley.edu/~jordan/courses/260-spring10/lectures/lecture14.pdf). It's usual to work with a matrix model $y = X\\beta + \\epsilon$ so in our notation we get\n", "\n", "$$ \\begin{pmatrix} y_1 \\\\ y_2 \\\\ \\vdots \\\\ y_n \\end{pmatrix} =\n", "\\begin{pmatrix} 1 & x_1 \\\\ 1 & x_2 \\\\ \\vdots & \\vdots \\\\ 1 & x_n \\end{pmatrix}\n", "\\begin{pmatrix} a \\\\ b \\end{pmatrix}\n", "+ \\begin{pmatrix} \\epsilon_1 \\\\ \\epsilon_2 \\\\ \\vdots \\\\ \\epsilon_n \\end{pmatrix} $$\n", "\n", "For reference, then\n", "\n", "$$ X^TX = \\begin{pmatrix} n & \\sum_i x_i \\\\ \\sum_i x_i & \\sum_i x_i^2 \\end{pmatrix} \n", "\\implies\n", "(X^TX)^{-1} = \\frac{1}{n^2\\sigma_x^2} \\begin{pmatrix} \\sum_i x_i^2 & -\\sum_i x_i \\\\ -\\sum_i x_i & n \\end{pmatrix}\n", "$$\n", "\n", "We'll introduce what you might call a \"hyper-parameter\" $g$, with here $p(g) \\propto g^{-3/2} \\exp(-n/2g)$ (an [Inverse Gamma distribution](https://en.wikipedia.org/wiki/Inverse-gamma_distribution)) and then\n", "\n", "$$ \\beta \\sim N(0, g\\sigma^2 (X^TX)^{-1}). $$\n", "\n", "We also put the Jeffrey's prior $p(\\sigma) \\propto 1/\\sigma$ on $\\sigma$. Thus the Posterior is\n", "\n", "\\begin{align*} p(\\beta,\\sigma,g | y) &\\propto p(y|\\beta,\\sigma,g) p(\\beta,\\sigma,g)\n", "= p(y|\\beta,\\sigma,g) p(\\beta|\\sigma,g) p(\\sigma) p(g) \\\\\n", "&\\propto \\prod (2\\pi\\sigma^2)^{-1/2} \\exp\\Big(-\\frac{1}{2\\sigma^2} (y_i - (X\\beta)_i)^2 \\Big)\n", " \\frac{\\sqrt{\\det(X^TX)}}{2\\pi g\\sigma^2} \\exp\\Big(-\\frac{1}{2g\\sigma^2} \\beta^TX^TX\\beta\\Big)\n", " \\frac{1}{\\sigma} g^{-3/2} \\exp(-n/2g) \\\\\n", "&\\propto \\prod (2\\pi\\sigma^2)^{-1/2} \\exp\\Big(-\\frac{1}{2\\sigma^2} (y_i - a - bx_i)^2 \\Big)\n", " \\frac{1}{g\\sigma^2} \\exp\\Big(-\\frac{1}{2g\\sigma^2} \\sum_i (a+bx_i)^2\\Big)\n", " \\frac{1}{\\sigma} g^{-3/2} \\exp(-n/2g)\n", "\\end{align*}" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def log_prior(theta):\n", " a, b, sigma, g = theta\n", " if g <= 0:\n", " return -np.inf\n", " beta_prior = -np.log(g * sigma**2) - np.sum( (a + b * x)**2 ) / ( 2 * g * sigma**2 )\n", " sigma_prior = - np.log(abs(sigma))\n", " g_prior = - 1.5 * np.log(g) - len(x) / (2 * g)\n", " return beta_prior + sigma_prior + g_prior\n", "\n", "def log_prob(theta, x, y):\n", " lp = log_prior(theta)\n", " if not np.isfinite(lp):\n", " return -np.inf\n", " return lp + log_likelihood(theta[:3], x, y)\n", "\n", "ndim, nwalkers = 4, 50\n", "sampler = emcee.EnsembleSampler(nwalkers, ndim, log_prob, args=[x, y])\n", "\n", "starting_guesses = np.random.normal(0, 0.1, (nwalkers, ndim)) + [a_est, b_est, sigma_est, 1]\n", "sampler.run_mcmc(starting_guesses, 2000)\n", "emcee_trace = sampler.chain[:, 1000:, :].reshape(-1, ndim).T" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 112 }, { "cell_type": "code", "collapsed": false, "input": [ "figure = triangle.corner(emcee_trace.T, labels=[\"$a$\", \"$b$\", \"$\\sigma$\", \"$g$\"], truths=[5, 3, 8, 1])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAApsAAAKbCAYAAAC6kkFkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nsVgsFovFYvEbVtm0WCwWi8VisfiN/wdjARFU7v3tMAAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 113 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's just marginalise over $g$, to get the following." ] }, { "cell_type": "code", "collapsed": false, "input": [ "figure = triangle.corner(emcee_trace[:3,:].T, labels=[\"$a$\", \"$b$\", \"$\\sigma$\"], truths=[5, 3, 8])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAgQAAAIECAYAAABmAjaWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngDEEBoPBYDAYgP8PXEjBY9MDimoAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 114 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(figsize=(8,6))\n", "axes.set_xlim([0,50])\n", "plot_MCMC_model(axes, x, y, emcee_trace[:3,:])\n", "\n", "alpha, beta = emcee_trace[:2]\n", "print(\"Line:\", alpha.mean(), beta.mean())" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Line: 3.56815932092 3.05726399527\n" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAfgAAAF/CAYAAAClndsfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 115 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Perhaps as we might hope, this makes rather little difference." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Instead of attacking the same problem as elsewhere, I want to pick on a problem, again from the undergrad days1, that I felt unhappy with using the standard tools: it's a regression model.\n", "\n", "> A beaker of liquid is heated, and then removed from the source of heat and left to cool in a room whose temperature is 9 degrees. The temperature of the liquid is measured at the moment it is removed from the heat, and at intervals of 1 minute thereafter. The following results are observed:\n", "\n", "Time (mins) | 0 | 1 | 2 | 3 | 4 | 5 | 6\n", " ------------|---|---|---|---|---|---|---\n", " Temperature | 100 | 82 | 60 | 50 | 40 | 32 | 28\n", "\n", "> Setup and study an appropriate regression model.\n", "\n", "\n", "1Can you tell I've been brushing up on my probability and statistics recently?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The relevant bit of Physics here is [Newton's Law of Cooling](https://en.wikipedia.org/wiki/Convective_heat_transfer#Newton.27s_law_of_cooling): \"the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings.\" This means that\n", "$$ \\frac{dT}{dt} = -r(T-T_e)$$\n", "where $T$ is the temperature, $t$ is time, $T_e$ is the temperature of the \"environment\" (our room) and $r>0$ is a constant depending on the beaker and the liquid and the room (and which we presumably wish to estimate from our data).\n", "\n", "The solution to this differential equation is\n", "$$ T(t) - T_e = (T(0)-T_e) \\exp(-rt). $$\n", "We're told that $T_e = 9$, and so $T(t) = 9 + (T(0)-9)\\exp(-rt)$.\n", "\n", "From now on, write $\\Delta T = T - T_e = T - 9$. The data becomes\n", "\n", "\n", "Time (mins) | 0 | 1 | 2 | 3 | 4 | 5 | 6\n", " ------------|---|---|---|---|---|---|---\n", "$\\Delta T$ | 91 | 73 | 51 | 41 | 31 | 23 | 19" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "How to setup a statistical model?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Perhaps the temperature of 100 degrees (Celcius) at the start is [red herring](https://en.wikipedia.org/wiki/Red_herring).\n", "\n", " - Our model will presumably take account of the guess that the thermometer is not 100% accurate, but rather has an error term attached to it.\n", " - (Maybe we should also model the _time_ as having an error term?)\n", "\n", "So, 100 degrees at the start might make us think of boiling water, and so treat this as an _accurate_ measure. But I don't think we should: all the readings should have an error.\n", "\n", " - A more sophisticated idea might be that the error of the therometer is affected by the temperature: perhaps readings near 0 are more accurate than near 100?\n", " - Might we also worry about the room temperature being definitely 9 degrees (if the same thermometer has been used)??\n", " \n", "A **silly** way to setup a standard regression model is to note that\n", "$$ \\frac{T(t)-9}{T(0)-9} = e^{-rt} \\implies \\log\\Big(\\frac{T(t)-9}{T(0)-9}\\Big) = -rt.$$\n", "This then gives us data which we can plug into a least-squares regression model. However, I see a problem here:\n", "\n", " - Let $x_i$ be the measured value of $\\Delta T$ at time $t_i$.\n", " - Naively we set $y_i = \\log( x_i / x_0 ) = \\log x_i - \\log x_0$.\n", " - This immediately creates a problem, as $y_0 = 0$ and so we effectively lose one data point.\n", " - The standard linear regression model is that $y_i = -rt_i + e_i$ with $e_i$ being an error term, typically modelled as $e_i \\sim N(0,\\sigma^2)$.\n", " - However, it's really $\\Delta T(t_i)$ which we measure and which has the error, say giving $x_i = \\Delta T(t_i) + \\epsilon_i$ with $\\epsilon_i$ the measurement error.\n", " - Then $$e_i = y_i + rt_i = \\log\\Big(\\frac{x_i}{x_0}\\Big) - \\log\\Big(\\frac{\\Delta T(t_i)}{\\Delta T(0)}\\Big) = \\log\\Big(\\frac{x_i}{x_0}\\Big) - \\log\\Big(\\frac{x_i - \\epsilon_i}{x_0 - \\epsilon_0}\\Big) = \\log\\Big(\\frac{x_i}{x_i - \\epsilon_i}\\Big) - \\log\\Big(\\frac{x_0}{x_0 - \\epsilon_i}\\Big). $$\n", " - So it's incredibly unclear what sort of errors on $\\epsilon_i$ would give rise to $e_i \\sim N(0,\\sigma^2)$. Furthermore, would the $(e_i)$ be _independent_?" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "The \"correct\" way to perform classical regression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Instead, let's re-arrange to get\n", "$$ \\log( \\Delta T(t_i) ) = \\log(\\Delta T(0)) - rt_i. $$\n", "So setting $y_i$ to be the measured value of $\\log( \\Delta T(t_i) )$ we have a regression model $y_i = a - rt_i + e_i$. (Then $y_0 = a + e_0$ so we treat the initial reading in a more \"symmetric\" way).\n", "\n", "I still find this problematic, as again, let $x_i$ be the reading of $\\Delta T(t_i)$, so $x_i = \\Delta T(t_i) + \\epsilon_i$ with an error term. Then\n", "$$ \\Delta T(t_i) + \\epsilon_i = x_i = \\exp(y_i) = e^a e^{-rt_i} \\exp(e_i) = \\Delta T(t_i) \\exp(e_i). $$\n", "Thus\n", "$$ \\epsilon_i = \\Delta T(t_i)\\big( e^{e_i} - 1 \\big). $$\n", "\n", "If $X\\sim N(0,\\sigma^2)$ and $Y = \\alpha(e^X-1)$ for some $\\alpha > 0$ then $Y$ has the following density\n", "$$ f_Y(y) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\frac{1}{y+\\alpha} \\exp\\Big( -\\frac{1}{2\\sigma^2}\\log\\Big(\\frac{t}{\\alpha}+1\\Big)^2 \\Big), $$\n", "supported on $y/\\alpha + 1 > 0$ or $y > -\\alpha$. This is a shifted [Log Normal](https://en.wikipedia.org/wiki/Log-normal_distribution) distribution." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# alpha = 1, sigma = 1\n", "y = np.arange(-0.99, 2, 0.01)\n", "f = np.exp(-0.5 * np.log(y+1) * np.log(y+1)) / (y + 1) / np.sqrt(2 * np.pi)\n", "plt.plot(y,f)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 6, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEACAYAAABI5zaHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ " - I don't see why we should model a thermometer with this sort of distribution (with the error scaling with the reading, and in our setup, this means that as the temperature approaches the measured environment temperature, the error drops to zero).\n", " - OTOH, presumably our thermometer _is_ giving a fixed, consistent reading of the temperature of the environment!\n", " \n", "Anyway, for the sake of doing some Bayesian analysis, let's suppose the errors in our readings, $\\epsilon_i$, are distributed $N(0,\\sigma^2)$." ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Some simulation" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def exact(T0, r, ti):\n", " Ti = T0 * np.exp(-r * ti)\n", " return Ti\n", "\n", "def simulate(T0, r, ti, variance):\n", " Ti = T0 * np.exp(-r * ti)\n", " Ti += np.random.normal(0, np.sqrt(variance), Ti.size)\n", " return Ti" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "simulate(91, 0.26, np.arange(0,7), 0.00001)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 3, "text": [ "array([ 90.9949331 , 70.16341598, 54.1047304 , 41.70874508,\n", " 32.16502375, 24.79957468, 19.12166433])" ] } ], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "simulate(91, 0.26, np.arange(0,7), 5)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [ "array([ 97.00893952, 71.49114008, 56.27001536, 43.71170836,\n", " 36.91663608, 25.04277522, 21.88228346])" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Naive regression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In our naive model, we have $Y_i = \\log \\Delta T(t_i) + e_i$ and the maximum likelihood estimates for $a$ and $r$ are:\n", "$$ \\hat r = - \\Big( \\sum_i (t_i - \\overline t)(y_i - \\overline y) \\Big) / \\Big( \\sum_i (t_i - \\overline t)^2 \\Big),\n", "\\qquad \\hat a = \\overline y + \\hat r \\overline t. $$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def naive_regress(yi, ti):\n", " \"\"\"Returns (a,r)\"\"\"\n", " tmean = np.sum(ti) / ti.size\n", " ymean = np.sum(yi) / yi.size\n", " r = - np.sum((ti - tmean) * (yi - ymean)) / np.sum((ti - tmean)**2)\n", " a = ymean + r * tmean\n", " return a, r\n", "\n", "ti = np.arange(0,7)\n", "Ti = simulate(91, 0.26, ti, 5)\n", "xi = np.log(Ti)\n", "a_naive, r_naive = naive_regress(xi, ti)\n", "print(a_naive, r_naive, \"-->\", np.exp(a_naive), r_naive)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "4.54473069836 0.275487935096 --> 94.135073066 0.275487935096\n" ] } ], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(1, 2, figsize=(15, 5))\n", "_ = axes[0].plot(ti, a_naive - r_naive * ti, lw = 2)\n", "_ = axes[0].plot(ti, xi, lw = 3)\n", "_ = axes[1].plot(ti, np.exp(a_naive - r_naive * ti), lw = 2)\n", "_ = axes[1].plot(ti, Ti, lw = 3)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAA2gAAAE4CAYAAAAuB9DjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Bayesian approach" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "My model is that $x_i = \\Delta T(t_i) + \\epsilon_i$ with $\\epsilon_i \\sim N(0,\\sigma^2)$. So $X_i \\sim N(e^{a-rt_i}, \\sigma^2)$, and thus\n", "$$ \\mathbb P(x|a, r, \\sigma^2) = \\prod_i \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp\\Big( -\\frac{(x_i - e^{a-rt_i})^2}{2\\sigma^2} \\Big). $$\n", "\n", "I'll just use the Jeffrey's prior on $\\sigma$ and flat priors on $a,b$." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def log_likelihood(theta, ti, Ti):\n", " a, r, sigma = theta\n", " return - np.sum((Ti - np.exp(a - r * ti))**2) / (2 * sigma**2) - Ti.size * np.log(sigma*sigma) * 0.5\n", "\n", "log_likelihood((np.log(91), 0.26, 5), ti, Ti)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 7, "text": [ "-11.704905380534159" ] } ], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "import scipy.optimize as op\n", "nll = lambda *args: -log_likelihood(*args) # Minimise the negative to get the maximum!\n", "result = op.minimize(nll, [np.log(91), 0.26, 5], args=(ti, Ti))\n", "a_est, r_est, sigma_est = result[\"x\"]\n", "print(np.exp(a_est), r_est, sigma_est, \"-->\", log_likelihood((a_est, r_est, sigma_est), ti, Ti) )" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "92.085032471 0.265229447515 1.69725825583 --> -7.20309913771\n" ] } ], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "def log_prior(theta):\n", " a, b, sigma = theta\n", " if sigma <= 0:\n", " return -np.inf\n", " return - np.log(sigma)\n", "\n", "def log_prob(theta, ti, Ti):\n", " lp = log_prior(theta)\n", " if not np.isfinite(lp):\n", " return -np.inf\n", " return lp + log_likelihood(theta, ti, Ti)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "import emcee\n", "ndim, nwalkers = 3, 50\n", "sampler = emcee.EnsembleSampler(nwalkers, ndim, log_prob, args=[ti, Ti])\n", "\n", "starting_guesses = np.random.normal(0, 0.1, (nwalkers, ndim)) + [a_est, r_est, sigma_est]\n", "sampler.run_mcmc(starting_guesses, 2000)\n", "emcee_trace = sampler.chain[:, 1000:, :].reshape(-1, ndim).T" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 15 }, { "cell_type": "code", "collapsed": false, "input": [ "import triangle\n", "figure = triangle.corner(emcee_trace.T, labels=[\"$a$\", \"$r$\", \"$\\sigma$\"], truths=[np.log(91), 0.26, 5])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAgIAAAICCAYAAAC9RaXMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nZ7ZaSQAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(figsize=(12, 5))\n", "_ = axes.plot(ti, Ti, \"ok\")\n", "\n", "x = np.linspace(0,6,30)\n", "a, r = emcee_trace[:2]\n", "y = np.exp(a[:,None] - r[:,None]*x)\n", "mu = y.mean(0)\n", "s = y.std(0)\n", "_ = axes.plot(x, mu, color=\"black\")\n", "_ = axes.fill_between(x, mu - s, mu + s, color='lightgray')\n", "_ = axes.plot(ti, np.exp(a_naive - r_naive * ti))\n", "_ = axes.legend([\"Data\", \"Bayesian\", \"naive\"])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAsMAAAE4CAYAAAC+Mf4FAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "For the original problem" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Ti = np.array( [91, 73, 51, 41, 31, 23, 19] )\n", "ti = np.array( range(7) )\n", "xi = np.log(Ti)\n", "a_naive, r_naive = naive_regress(xi, ti)\n", "print(a_naive, r_naive, \"-->\", np.exp(a_naive), r_naive)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "4.51298712746 0.26810823074 --> 91.1938196201 0.26810823074\n" ] } ], "prompt_number": 18 }, { "cell_type": "code", "collapsed": false, "input": [ "nll = lambda *args: -log_likelihood(*args) # Minimise the negative to get the maximum!\n", "result = op.minimize(nll, [np.log(91), 0.26, 5], args=(ti, Ti))\n", "a_est, r_est, sigma_est = result[\"x\"]\n", "print(np.exp(a_est), r_est, sigma_est, \"-->\", log_likelihood((a_est, r_est, sigma_est), ti, Ti) )" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "91.9417249709 0.271455483938 1.54476101614 --> -6.54408505649\n" ] } ], "prompt_number": 19 }, { "cell_type": "code", "collapsed": false, "input": [ "ndim, nwalkers = 3, 50\n", "sampler = emcee.EnsembleSampler(nwalkers, ndim, log_prob, args=[ti, Ti])\n", "\n", "starting_guesses = np.random.normal(0, 0.1, (nwalkers, ndim)) + [a_est, r_est, sigma_est]\n", "sampler.run_mcmc(starting_guesses, 2000)\n", "emcee_trace = sampler.chain[:, 1000:, :].reshape(-1, ndim).T\n", "\n", "figure = triangle.corner(emcee_trace.T, labels=[\"$a$\", \"$r$\", \"$\\sigma$\"])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAgIAAAICCAYAAAC9RaXMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n3gXH3BmgkAAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 26 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(figsize=(12, 5))\n", "_ = axes.plot(ti, Ti, \"ok\")\n", "\n", "x = np.linspace(0,6,30)\n", "a, r = emcee_trace[:2]\n", "y = np.exp(a[:,None] - r[:,None]*x)\n", "mu = y.mean(0)\n", "s = y.std(0)\n", "_ = axes.plot(x, mu, color=\"black\")\n", "_ = axes.fill_between(x, mu - s, mu + s, color='lightgray')\n", "_ = axes.plot(ti, np.exp(a_naive - r_naive * ti))\n", "_ = axes.legend([\"Data\", \"Bayesian\", \"naive\"])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAsMAAAE4CAYAAAC+Mf4FAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 27 }, { "cell_type": "code", "collapsed": false, "input": [ "a, r = emcee_trace[:2]\n", "print(\"Naive regression r:\", r_naive, \"Bayesian model r:\", r.mean())" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Naive regression r: 0.26810823074 Bayesian model r: 0.272503086349\n" ] } ], "prompt_number": 28 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }