{ "cells": [ { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy as sp\n", "import scipy.stats\n", "import matplotlib.pyplot as plt\n", "import random as rm\n", "import pymc\n", "import arviz as az\n", "\n", "plt.style.use(\"fivethirtyeight\")\n", "\n", "import warnings\n", "\n", "warnings.filterwarnings(\"ignore\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Bayesian is not the opposite of frequentist, but it holds a contrasting view comparing with frequentists.\n", "\n", "In the first chapter, we review Bayes' Theorem and provide an overview of application in statistics and econometrics.\n", "\n", "If all you want know is what Bayesian framework is, this is the only chapter you need to read." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Bayesian Theory " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The bayesian theory is built upon the most famous **Bayes' Theorem**, which is derived from condition probability and joint probability.\n", "\n", "The **law of joint probability** says that\n", "$$\n", "P(x, y)=P(x \\mid y) P(y)\n", "$$\n", "or \n", "$$\n", "P(x, y)=P(y \\mid x) P(x)\n", "$$\n", "Combine them, we will obtain the formula of Bayes' Theorem.\n", "$$\n", "P(x \\mid y)=\\frac{P(y \\mid x) P(x)}{P(y)}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To make it meaningful in the context of statistics/econometrics, replace the symbols will provide a refreshing view\n", "$$\n", "P(\\theta \\mid Y)=\\frac{P(Y \\mid \\theta) P(\\theta)}{P(Y)}\n", "$$\n", "where $Y$ is the data, $\\theta$ is the vector of parameters you would like to make inferrence. The formula summarizes what we know about $\\theta$ about having seen the sample of observations on $Y$.\n", "\n", "In Bayesian terms\n", "\\begin{align}\n", "\\text{prior:}&\\ P(\\theta)\\\\\n", "\\text{likelihood:}&\\ P(Y|\\theta)\\\\\n", "\\text{marginal likelihood:}&\\ P(Y)\\\\\n", "\\text{posterior:}&\\ P(\\theta|Y)\\\\\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To update prior beliefs into posterior beliefs conditional on observed data, the process is called **Bayesian Inference**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "More often, we ignore $P(Y)$ due to its irrelevance to $\\theta$, the formula simplies into\n", "$$\n", "P(\\theta \\mid Y) \\propto P(Y \\mid \\theta) P(\\theta)\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Model Comparison " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you have multiple models in mind, Bayesian framework can provide model comparison too. Suppose we have $m$ different models, $M_i$ for $i=1, ..., m$, the posterior for the parameters calculated using $M_i$ is \n", "$$\n", "P\\left(\\theta^{i} \\mid Y, M_{i}\\right)=\\frac{P\\left(Y \\mid \\theta^{i}, M_{i}\\right) P\\left(\\theta^{i} \\mid M_{i}\\right)}{P\\left(Y \\mid M_{i}\\right)}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use $i$ to signal that for each model has its own posterior, likelihood and prior." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, to compare models, we need to evaluate the **posterior model probability**\n", "$$\n", "\\operatorname{P}\\left(M_{i} \\mid Y\\right) \\propto P\\left(Y \\mid M_{i}\\right) \\operatorname{P}\\left(M_{i}\\right),\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose there are two competing models, the **posterior odds ratio** is constructed as\n", "$$\n", "\\frac{P\\left(M_{1} \\mid Y\\right)}{P\\left(M_{2} \\mid Y\\right)}=\\frac{P\\left(Y \\mid M_{1}\\right)}{P\\left(Y \\mid M_{2}\\right)} \\frac{P\\left(M_{1}\\right)}{P\\left(M_{2}\\right)}\n", "$$\n", "Specifically, this part is called **Bayes factor**\n", "$$\n", "BF_{12}=\\frac{P\\left(Y \\mid M_{1}\\right)}{P\\left(Y \\mid M_{2}\\right)} \n", "$$\n", "which is a the ratio of _marginal likelihoods_ for model $1$ and model $2$. Furthermore, marginal likelihood can be decomposed into\n", "$$\n", "P\\left(Y \\mid M_{i}\\right)=\\int_{\\theta_{i}} P\\left(Y \\mid \\theta_{i}, M_{i}\\right) P\\left(\\theta_{i} \\mid M_{i}\\right) d \\theta_{i}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "# Bernoulli Example " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Likelihood " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An example will help clarify how we use the Bayes' Theorem for inference and prediction. \n", "\n", "The Bernoulli PMF is commonly written as\n", "$$\n", "f(k; p) = p^{k}(1-p)^{1-k}\\ \\text{ for }\\ \\ k\\in \\{0, 1\\}\n", "$$\n", "Watch out for the notation, that $k$ equals either $0$ or $1$, not $k \\in (0, 1)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The meaning of $0$ and $1$ usually represent \"happened\" and \"not happened\". Now suppose we have collects a sample $K= (k_1, k_2, k_3,...,k_T)$. \n", "\n", "The joint Bernoulli PMF is the multiplication of them due to independence assumption\n", "$$\n", "f(K|p)=p^{k_1}(1-p)^{1-k_1}p^{k_2}(1-p)^{1-k_2}p^{k_3}(1-p)^{1-k_3}...p^{k_T}(1-p)^{1-k_T}=p^{\\sum_{i=0}^T k_i}(1-p)^{T-\\sum_{i=0}^T k_i}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "which is the **likelihood function** given all possible $p$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Prior " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We need **prior** too.\n", "\n", "The most frequently used prior in Bayesian inference is **Beta distribution**, because it naturally models the _probability of a probability_. \n", "\n", "For instance, you can ask a question, what's the probability that a random person has diabetes? You could give an educated guess around $30\\%$, then you go to collect data on the street that asking random person provide a blood sample test.\n", "\n", "Recall that we have mentioned pdf of Beta distribution\n", "\\begin{equation}\n", "f(p, \\alpha, \\beta)=\\frac{\\Gamma(\\alpha+b) p^{\\alpha-1}(1-p)^{\\beta-1}}{\\Gamma(\\alpha) \\Gamma(\\beta)}\n", "\\end{equation}\n", "However in Bayesian inference, we usually combine those gamma functions into a beta function term.\n", "\\begin{equation}\n", "f(p, \\alpha, \\beta)=\\frac{1}{B(\\alpha, \\beta)} p^{\\alpha-1}(1-p)^{\\beta-1}\n", "\\end{equation}\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Posterior " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Posterior is straightforward by evoking Bayes' Theorem.\n", "$$\n", "f(p|K) \\propto \\left(p^{\\sum_{i=0}^T k_i}(1-p)^{T-\\sum_{i=0}^T k_i}\\right)\\frac{1}{B(\\alpha_0, \\beta_0)} p^{\\alpha_0-1}(1-p)^{\\beta_0-1}\n", "$$\n", "where subscript $0$ represent **prior**.\n", "\n", "Since we have already using $\\propto$, we only need to keep the kernel of beta distribution, which simplifies to\n", "$$\n", "f(p|K) \\propto \\left(p^{\\sum_{i=0}^T k_i}(1-p)^{T-\\sum_{i=0}^T k_i}\\right) p^{\\alpha_0-1}(1-p)^{\\beta_0-1}\n", "$$\n", "Collect terms we obtain the kernel of posterior distribution, which is also a beta distribution!\n", "$$\n", "f(p|K) \\propto p^{\\sum_{i=0}^T k_i+\\alpha_0-1}(1-p)^{T-\\sum_{i=0}^T k_i+\\beta_0-1}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will see more detailed examples in next chapter, we just derived posterior analytically by using **conjugate prior**, whose posterior takes the same function form, but with updated parameters. \n", "\n", "In this case the posterior parameters are updated to\n", "$$\n", "\\alpha=\\sum_{i=0}^T k_i+\\alpha_0\\\\\n", "\\beta=T-\\sum_{i=0}^T k_i+\\beta_0\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plug in Numbers " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's plug in some numbers for the parameters and try plotting the distribution. \n", "\n", "The beta distribution models our prior belief, let's say the parameters are set as\n", "$$\n", "\\alpha_0 = 4\\\\\n", "\\beta_0 = 7\n", "$$\n", "The sample is \n", "$$\n", "K= (1, 0, 0, 0, 1, 0, 1, 1, 0, 0)\n", "$$\n", "whose sample size is $T=10$. Therefore the posterior parameters are\n", "$$\n", "\\alpha = 4+4=8\\\\\n", "\\beta=10-4+7=13\n", "$$\n", "Plot prior and posterior together. " ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x_beta = np.linspace(0, 1, 200)\n", "y_beta_prior = sp.stats.beta(a=4, b=7).pdf(x_beta)\n", "y_beta_posterior = sp.stats.beta(a=8, b=13).pdf(x_beta)\n", "\n", "fig, ax = plt.subplots(figsize=(6, 6))\n", "ax.plot(x_beta, y_beta_prior, label=\"prior\")\n", "ax.fill_between(x_beta, y_beta_prior, alpha=0.5)\n", "ax.plot(x_beta, y_beta_posterior, label=\"posterior\")\n", "ax.fill_between(x_beta, y_beta_posterior, alpha=0.5)\n", "ax.set_title(\"Beta-Bernoulli Conjugate\")\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Coin Example " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Throwing coins is a perfect illustration for Bayesian conjugates with Bernoulli likelihood. Suppose you suspect a coin is unfair, which means not the usual $50/50$ chances. \n", "\n", "You can have any theory you want, here we have function for plot example plots that you can define your prior for Beta distribution namely $\\alpha_0$ and $\\beta_0$, also you can determine if the coin is really unfair by tweaking probability of success in Bernoulli function, we named it ```fairness```, a fair coin would have it equal to $.5$." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "def plot_coins_with_prior(a_prior, b_prior, fairness):\n", " number_of_trials = [0, 5, 15, 20, 30, 100]\n", " x = np.linspace(0, 1, 100)\n", " plt.figure(figsize=(16, 7))\n", " for i, N in enumerate(number_of_trials):\n", " heads = np.sum(sp.stats.bernoulli.rvs(p=fairness, size=N))\n", " ax = plt.subplot(int(len(number_of_trials) / 3), 3, i + 1)\n", " ax.set_title(\"{} trials, {} heads\".format(N, heads))\n", "\n", " plt.xlabel(\"$P(H)$, Probability of Heads\")\n", " plt.ylabel(\"Density\")\n", " if i == 0:\n", " plt.ylim([0.0, 2.0])\n", " plt.setp(ax.get_yticklabels(), visible=False)\n", "\n", " y = sp.stats.beta.pdf(\n", " x, heads + a_prior, N - heads + b_prior\n", " ) # post_a = sum of heads + 1, post_b = times - sum of heads + 1\n", " plt.plot(\n", " x, y, label=\"observe %d tosses,\\n %d heads\" % (N, heads), color=\"orange\"\n", " )\n", " plt.fill_between(x, 0, y, color=\"tomato\", alpha=0.7)\n", " plt.suptitle(\n", " r\"Hyperparameters: $\\alpha_0={},\\beta_0={}$, Likelihood parameter p={}\".format(\n", " a_prior, b_prior, fairness\n", " ),\n", " size=23,\n", " )\n", " plt.tight_layout(pad=0.6)\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_coins_with_prior(a_prior=1, b_prior=3, fairness=0.7)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Reporting Results " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can provide numerical features of posterior distribution such as mean and standard deviation as **point estimates**. Because the posterior are not simulated, we have formula for mean and variance which can be found from any textbook or Wikipedia.\n", "$$\n", "\\mathrm{E}[X]=\\frac{\\alpha}{\\alpha+\\beta}\\\\\n", "\\operatorname{var}[X]=\\frac{\\alpha \\beta}{(\\alpha+\\beta)^{2}(\\alpha+\\beta+1)}\n", "$$" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "mean of posterior: 0.38095238095238093\n", "std of posterior: 0.010719439290867862\n" ] } ], "source": [ "a, b = 8, 13\n", "mean_post = a / (a + b)\n", "std_post = (a * b) / ((a + b) ** 2 * (a + b + 1))\n", "print(\"mean of posterior: {}\".format(mean_post))\n", "print(\"std of posterior: {}\".format(std_post))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Bayesian Credible Interval** is another common statistic that usually provided in some statistic software. The Bayesian Credible Interval differs the Frequentist Confidence Interval mostly in a philosophical sense.\n", "\n", "Frequentists assume the parameters are fixed but confidence intervals are random, so $95\\%$ confidence interval means if the experiment repeats $100$ times, there are round $95$ times the confidence interval will include the true parameter. \n", "\n", "However Bayesian holds a contrasting view that parameters are random, but the credible intervals are fixed. As an example, the shaded are is the $95\\%$ credible interval. It indicates that there is $95\\%$ chance the interval include the true parameter." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lb = sp.stats.beta(a=8, b=13).ppf(0.025)\n", "ub = sp.stats.beta(a=8, b=13).ppf(0.975)\n", "x_ci = np.linspace(lb, ub, 100)\n", "y_ci = sp.stats.beta(a=8, b=13).pdf(x_ci)\n", "\n", "x_beta = np.linspace(0, 1, 100)\n", "y_beta_posterior = sp.stats.beta(a=8, b=13).pdf(x_beta)\n", "\n", "fig, ax = plt.subplots(figsize=(6, 6))\n", "ax.plot(x_beta, y_beta_posterior, color=\"orange\")\n", "ax.fill_between(x_ci, y_ci, color=\"tomato\", alpha=0.5)\n", "\n", "ax.set_title(\"Bayesian Credible Interval\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Numerical Methods " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Most of time you won't achieve an analytical form of posterior, this is where computer simulation comes in.\n", "\n", "There are mainly two categories of numerical methods for Bayesian posterior simulation, i.e. **Markovian** and **Non-Markovian** methods. The former is the industrial standard for Bayesian framework, the latter is easier to intuitive and code-friendly too. \n", "\n", "We will illustrate some examples of Non-Markovian examples, in later chapters, we will go in to depth of Markovian methods." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Grid Computing " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Grid computing is a straightforward brute-force approach, you basically sample the probability density or mass function of priors and likelihood, then you obtain posterior by multiplying them.\n", "\n", "Here we also use the coin-flipping example, but note that we change from flipping once to multiple times, naturally the binomial distribution will replace Bernoulli.\n", "\n", "The algorithm is very intuitive\n", "1. You define equidistant range for prior.\n", "2. Calculate mass or density for each point (grids).\n", "3. Multiply likelihood and prior." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "def posterior_grid_coins(grid_points, heads, tosses, alpha, beta):\n", " grid = np.linspace(0, 1, grid_points)\n", " prior = sp.stats.beta(a=alpha, b=beta).pdf(grid)\n", " prior = prior / np.sum(prior)\n", " likelihood = sp.stats.binom.pmf(heads, tosses, grid)\n", " posterior = (likelihood * prior) / np.sum(likelihood * prior) # normalize the unit\n", " return grid, prior, posterior" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "grid_points, heads, tosses, alpha, beta = 100, 25, 100, 6, 8\n", "grid, prior, posterior = posterior_grid_coins(grid_points, heads, tosses, alpha, beta)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(5, 5))\n", "ax.plot(grid, prior, label=r\"prior: Beta $\\alpha={}$, $\\beta={}$\".format(alpha, beta))\n", "ax.fill_between(grid, prior, color=\"lightblue\", alpha=0.8)\n", "\n", "ax.plot(grid, posterior, label=\"posterior\")\n", "ax.fill_between(grid, posterior, color=\"tomato\", alpha=0.5)\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However fast and simple, this method is not practical in higher dimension due to **curse of dimensionality**. This is easier to understand with our example here, we have $100$ grid points for one dimension distribution, if we use the same amount of grid points for two dimension distribution the grid points will be $10000$, basically $N^p$, where $N$ is number of grid point for each variable, $p$ is the dimension or the number of random variables. To sample every also require to increase the number of samples to increase exponentially, which is not feasible in practical modelling.\n", "\n", "Hence it is rarely a serious sampling tool rather a pedagogical gimmick." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Quadratic Method " ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "It's also called **Laplace approximation**, but more commonly called **quadratic method** which tells the essential part of the algorithm.\n", "\n", "If the posterior $p(\\theta)$ is a uni-modal distribution, the area around the mode usually are very close to a Gaussian distribution $q(\\theta)$ (go check all the posterior plots above and down). Theoretically, the posterior is asymptotically normal as the sample size goes to infinity. \n", "\n", "Once we find the mode, we measure the curvature around it (with _Hessian matrix_), equivalent to say that a rough estimate of $\\mu$ and $\\sigma$ of the posterior. To be specific, the algorithm follows two steps" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. Find the mode of $p(\\theta)$, the mode of posterior has Latin name **Maximum a-posteriori**, denoted by $\\hat{\\theta}_{MAP}$. We use it as the $\\mu$ of $q(\\theta)$.\n", "2. Measure the curvature near the mode of $p(\\theta)$ and use it to computer the $\\sigma$ of $q(\\theta)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For analytical purpose, some prefer to take log of posterior, therefore the area near the mode become a quadratic function which can be approximated by your chosen quadratic function." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The question now boils down to how to find the mode? If the posterior density function is $p(\\theta|y)$, we take the Taylor expansion of its log form centered at $\\hat{\\theta}_{MAP}$\n", "$$\n", "\\log p(\\theta \\mid y)=\\log p(\\hat{\\theta} \\mid y)+\\frac{1}{p(\\hat{\\theta} \\mid y)}(\\theta-\\hat{\\theta})+\\frac{1}{2}(\\theta-\\hat{\\theta})^{T}\\left[\\frac{d^{2}}{d \\theta^{2}} \\log p(\\theta \\mid y)\\right]_{\\theta=\\hat{\\theta}}(\\theta-\\hat{\\theta})+\\ldots\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Actually $\\frac{1}{p(\\hat{\\theta} \\mid y)}=0$, because it's the derivative at the $\\hat{\\theta}_{MAP}$. So it safely simplies to\n", "$$\n", "\\begin{align}\n", "\\log p(\\theta \\mid y)&=\\log p(\\hat{\\theta} \\mid y)+\\frac{1}{2}(\\theta-\\hat{\\theta})^{T}\\left[\\frac{d^{2}}{d \\theta^{2}} \\log p(\\theta \\mid y)\\right]_{\\theta=\\hat{\\theta}}(\\theta-\\hat{\\theta})+\\ldots\\\\\n", "&=\\log p(\\hat{\\theta} \\mid y)+\\frac{1}{2}(\\theta-\\hat{\\theta})^{T}\\boldsymbol{H}_{\\theta=\\hat{\\theta}}(\\theta-\\hat{\\theta})+\\ldots\n", "\\end{align}\n", "$$\n", "where $\\boldsymbol{H}$ is the Hessian matrix. Use the Hessian in the approximation Gaussian $q(\\theta)$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "q(\\theta)=\\frac{|\\boldsymbol{H}|^{1 / 2}}{(2 \\pi)^{N / 2}} \\exp \\left[-\\frac{1}{2}\\left(\\theta-\\hat{\\theta}\\right)^T \\boldsymbol{H}\\left(\\theta-\\hat{\\theta}\\right)\\right]\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The notation clearly shows that $\\boldsymbol{H}=\\boldsymbol{\\Sigma}^{-1}$, therefore the inverse of Hessian, i.e. $\\boldsymbol{H}^{-1}$ is the covariance matrix of $q(\\theta)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We won't go into much details here. There is ```pymc3.find_MAP()``` to obtain the $\\hat{\\theta}_{MAP}$." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "79dd2120b84349a19f87ef02826100d8", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Output()" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
\n",
       "
\n" ], "text/plain": [ "\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n",
       "
\n" ], "text/plain": [ "\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "coin_data = sp.stats.bernoulli(p=0.1).rvs(size=20)\n", "head = coin_data.sum()\n", "tail = len(coin_data) - head\n", "\n", "alpha_0, beta_0 = 3, 6\n", "with pymc.Model() as normal_approximation:\n", " p = pymc.Beta(\"p\", alpha_0, beta_0)\n", " w = pymc.Binomial(\"w\", n=1, p=p, observed=coin_data)\n", " mean_q = pymc.find_MAP()\n", " std_q = ((1 / pymc.find_hessian(mean_q, vars=[p])) ** 0.5)[0]\n", "MAP, sig = mean_q[\"p\"], std_q\n", "\n", "fig, ax = plt.subplots(figsize=(12, 5))\n", "# Use analytical posterior conjugacy\n", "x = np.linspace(0, 1, 100)\n", "ax.plot(\n", " x, sp.stats.beta(a=head + alpha_0, b=tail + beta_0).pdf(x), label=\"True posterior\"\n", ")\n", "\n", "# laplace approximation\n", "ax.plot(x, sp.stats.norm(loc=MAP, scale=sig).pdf(x), label=\"Quadratic approximation\")\n", "ax.axvline(x=MAP, label=\"MAP\", color=\"orange\")\n", "ax.legend(loc=0, fontsize=13)\n", "\n", "ax.set_title(\"heads = {}, tails = {}\".format(head, tail))\n", "ax.set_xlabel(r\"$\\theta$\", fontsize=14)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Metropolis Algo " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The simplest Markov Chain Monte Carlo is Metropolis algorithm. We will demonstrate the mechanism of it to sample a known distribution, which we pretend we know nothing of it. This has nothing to do with Bayesian estimation at all." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We need an initial value to start the chain, like we said, we know its median, so that could be the starting point, but even if we know nothing about it, we can make a guess too, just make sure the initial value fits in the range of the prior.\n", "\n", "Each new probability value will be evaluated by an acceptance rule." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This will be the acceptance rule we use\n", "$$\n", "p_a = \\frac{p^{ }_{new}}{p^{ }_{old}}\n", "$$\n", "then compare $p_a$ with a random draw from a uniform distribution.\n", "\n", "If $p_a$ larger than uniform draw, we accept it, otherwise we retreat to previous probability.\n", "\n", "Note that uniform distribution is always less than $1$, hence if $p^{ }_{new} > p^{ }_{old}$ we acceptance with $100\\%$. If $p_a=.8$, we have a $80\\%$ chance of accepting it." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "def metropolis(function, steps):\n", " sample = np.zeros(steps)\n", " old_x = 0.1 # [0, 1], if we use beta distribution\n", " old_prob = function.pdf(old_x) # calculate probability\n", " for i in range(steps):\n", " new_x = old_x + np.random.normal(\n", " 0, 1\n", " ) # give the previous value a disturbance, we use Gaussian\n", " new_prob = function.pdf(new_x) # update the probability\n", " acceptance = new_prob / old_prob # this is the acceptance rule\n", " if acceptance >= np.random.random():\n", " sample[i] = new_x\n", " old_x = new_x\n", " old_prob = new_prob\n", " else:\n", " sample[i] = old_x\n", " return sample" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "function = sp.stats.beta(2, 3)\n", "steps = 50000\n", "samples = metropolis(function, steps)\n", "\n", "pdf_curve = function.pdf(np.linspace(0, 1))" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(10, 10), ncols=1, nrows=2)\n", "ax[0].hist(samples, bins=100, density=True, histtype=\"step\", lw=2.5)\n", "ax[0].plot(np.linspace(0, 1), pdf_curve)\n", "ax[1].plot(samples, lw=0.5)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The upper chart is sampled distribution, lower chart is called the **trace**. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will discuss more MCMC methods such as Metropolis and Gibs Sampler in more details later. Here is an excellent reference material for visualizing the algorithm: https://chi-feng.github.io/mcmc-demo/" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## No U-Turn Sampler " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **No U-Turn Sampler** (NUTS) belongs to a bigger category which is called **Hamiltonian Monet Carlo** (HMC), which is actually very similar to **Metropolis-Hastings algorithm** (details in MCMC chapter, you can come bakc here after studying MCMC chapter), the key difference is the proposal distribution. \n", "\n", "But the intuition is extremely straightforward, watch the animation here: http://arogozhnikov.github.io/2016/12/19/markov_chain_monte_carlo.html. \n", "\n", "Imagine a bi-variate distribution which will can illustrated by 3D plot, the distribution will look like any terrain you have seen on a map, but upside down. Then a frictionless ball that follows the physical rule will be kicked to random direction, we record the location of ball after a pre-determined time say 3 seconds (you can choose any duration, but for the sake of efficiency, it should be too long or too short.) \n", "\n", "The intuition is that the ball will always tend to trace out lower area, in this case we flip the distribution upside down, which is the high density area. \n", "\n", "However HMC requires tuning parameters, but its close kin NUTS has free us from fiddling parameters, which is more accessible for broader background of users." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.0" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "toc-autonumbering": false, "toc-showmarkdowntxt": false }, "nbformat": 4, "nbformat_minor": 4 }