{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import scipy.stats\n", "import matplotlib.pyplot as plt\n", "from matplotlib import gridspec" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Bayesian inference\n", "\n", "In traditional, frequentist approach, we are interested in the probability of an event under known conditions. We may write it in the form $P(x\\mid\\theta)$, what means: probability of an event $x$ under the condition $\\theta$. For most cases $\\theta$ is a parameter or set of parameters of an probabilistic distribution, for example for normal distribution with mean $\\mu$ and variance $\\sigma^2$ we have:\n", "$$ P(x \\mid \\theta) \\sim P(x \\mid \\mu,\\,\\sigma^{2}) \\sim \\frac{1}{\\sqrt{2\\pi\\sigma^2}} e^{-\\frac{(x - \\mu)^2}{2 \\sigma^2}}.$$\n", "\n", "The Bayesian approach is an inverse one. Being given some observed events, we estimate the probability of parameters. It bases on the classical Bayes formula:\n", "\n", "$$ P(\\theta \\mid x) = \\dfrac{ P(x \\mid \\theta) P(\\theta) }{P(x)}.$$\n", "\n", "Traditionally, we use the names:\n", "- $ P(\\theta \\mid x) $ - *posterior probability*,\n", "- $ P(x \\mid \\theta) $ - *likelihood*,\n", "- $ P(\\theta) $ - *prior probability*,\n", "- $ P( x) $ - *evidence probability*.\n", "\n", "The evidence probability does not depend on $\\theta$ and provides only scaling factor for the posterior probability. It can be then ommited in most of the applications.\n", "\n", "One of the main weaknesses of the Bayesian inference is it's dependence on prior knowledge. In order to compute the likelihood, we need to know, up to the parameters, the probability distribution of the data. It also requires an initial guess on the parameter distribution, in order to evaluate prior.\n", "\n", "The Bayesian inference is often performed iteratively, that means that resulting posterior after every step of the iteration becomes the prior for the next step." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Radioactive decay with noisy background \n", "\n", "In the following exercises we will deal with real-live problem of determining the intensity of source decay in the presence of background noise. We assume that the number of registered counts follow the Poisson distributions with means respectively $\\lambda_{s}$ and $\\lambda_{b}$ for signal and background." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def get_background(lam_b = 30, s=1):\n", " return np.random.poisson(lam=lam_b, size = s)\n", "\n", "def get_background_signal(lam_b = 30, lam_s = 13, s = 1):\n", " return np.random.poisson(lam=lam_b+lam_s, size = s)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Ex 1.\n", "1. Implement likelihood function for poisson distribution.\n", "2. Assuming flat prior for background $\\lambda$ factor on [0,100] interval, calculate and plot posterior distributions for background $\\lambda$ after including 1-9 single background observations." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#1)\n", "def likelihood(lam, x):\n", " #here goes your code\n", "\n", "#test:\n", "#x = [30,32,34]\n", "#likelihood(30, x)\n", "#0.00025301172977209218" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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AiciAap6By0ZXr75BEOAcx2FoaKjtdScS/D4V8si7PsPDw8TjcU6dOrX5CxYR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\ngalUzMyhqaRux/a4YBy/HPtL/jjxj1Q2V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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#2)\n", "prior_bck = np.ones(100)/100\n", "prior_sg = np.ones(100)/100\n", "#here goes your code\n", "\n", "\n", "for i in range(9):\n", " data = get_background()\n", " #here goes your code\n", " \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Ex 2.\n", "1. Taking flat prior for signal $\\lambda$ parameter on [0,100] interval and posterior from Ex 1 for background, calculate and plot 2D posterior distribution for signal and background $\\lambda$ after including 1-9 single background-signal observations. Find lambdas which give the highest posterior." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#here goes your code\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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PazB+XoMZpkdO/Jw/YAdwbNfjY5ptkiTNO3ukJGlkpiH8fR44McnDk6wDngdc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\n9Hynf2pYhj9JQxnFeX/g6J8kSd1WCoE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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Optimal lambdas:\n" ] }, { "data": { "text/plain": [ "(10, 32)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#here goes your code\n", "\n", "#hint: plt.contourf(), np.unravel_index(posteriors[-1].argmax(), posteriors[-1].shape)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Loglikelihood\n", "\n", "Calculating likelihood is troublesome for large datasets due to low values of the probability and finite computer precision. Therefore, it is common to use the log-likelihood and log-posterior functions instead, which are equal to logarithms of the original ones. It helps us to avoid multiplying low numbers, which often leads to \"zero\" likelihood, as the logarithm of a product is a sum of logarithms. \n", "\n", "What is important, as logarithm is a monotonic function, the maximum of a function and log-function coincide.\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Try it:\n", "x = [23] * 100000\n", "likelihood(x, 30)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ex 3\n", "a) Implement the log-likelihood function for poisson distribution. \n", "b) Redo Ex 2 using log-posterior (single iteration, 9 samples). \n", "c) Plot results and verify that the maximum Log-posterior estimation gives similar results as posterior estimation." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#a)\n", "#here goes your code\n", "\n", "#test:\n", "#x = [23] * 100000\n", "#loglikelihood(x, 30)\n", "# -359340.98709556682" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/kacper/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:13: RuntimeWarning: divide by zero encountered in log\n", " del sys.path[0]\n" ] } ], "source": [ "#b)\n", "data = get_background_signal(s = 9)\n", "\n", "#here goes your code\n", "\n", "\n", "# logposterior is not loglikelihood * logprior !" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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cRSACAJNnigiwHQIRAOiCSITVmSJyNoEIAHRDJMLqRCKHCUQAoCsiEVYnEnmQ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\nlTupl0CE0amqxyT5pSTf11q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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Optimal lambdas:\n" ] }, { "data": { "text/plain": [ "(13, 32)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#c)\n", "#here goes your code\n", "#hint: plt.contourf(), np.unravel_index(logposterior.argmax(), logposteriors.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Bayes factor, p-value, $\\beta$\n", "\n", "While estimations and plots above can provide with us with suggestions about the distribution, we also need some numerical evaluation of conclusions which may be taken. In the following exercise we will study few of them." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ex 4.\n", "In all below we assume Poisson distribution. \n", "\n", "### Bayes factor\n", "Being given two hypothesies, $H_{0}$ (null hypothesis, default one) and $H_{1}$ (alternative hypothesis, the one which is being verified), we define the Bayes factor as:\n", "\n", "$$ K = \\dfrac{ P(x \\mid H_{1}) }{ P(x \\mid H_{0}) } $$\n", "\n", "High values of $K$ support the alternative hypothesis, low values reject it. One of the interpretation is as follows:\n", "\n", "| K | Strength of evidence|\n", "| :-------------:|:-------------:|\n", "| < $\\sqrt{10}$ | Negative |\n", "| $\\sqrt{10}$ - 10 | Substantial |\n", "| 10 - 100 | Strong |\n", "| >100 | Decisive |\n", "\n", "a) For number of counts from 10 to 50 calculate Bayes factor for $H_{0}: \\mu = 30$ (just background) nad $H_{1}: \\mu = 43$ (background + signal). Do the same for double counts (two identical results). " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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pBIqIiIiIHFF1GBb/Fj57GWJT4Kp3oet4p1PJKSo+VMWCDXlkebws2bKPymof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\n/h8ceUF6JlCSJEkZzxIo6f2rfA0e/CIkl8K4c9PLPwuKok4lSZKkD8A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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#here goes your code\n", "\n", "\n", "#hint: scipy.stats.poisson.pmf()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### P-value\n", "\n", "For a given observation and null hypothesis $H_{0}$, *P-value* is defined as a probability of observation at least as extreme as observed one under the condition, that $H_{0}$. Depending on the context and shape of the distribution, we may use:\n", "- left tail p-value: $P(x < x_{obs} \\mid H_{0})$,\n", "- right tail p-value: $P(x > x_{obs} \\mid H_{0})$,\n", "- two sided p-value: $2 \\min \\{ P(x < x_{obs} \\mid H_{0}), P(x > x_{obs} \\mid H_{0})\\} $.\n", "\n", "Low p-value is an indicator, that $H_{0}$ may be false. It is widely accepted, that p-value < 0.05 or < 0.01 is a sufficient to reject zero hypothesis. In certain fields, such as particle physics, much lower p-values are required.\n", "\n", "b) For count numbers from 10 to 50 calculate right-tailed p-value for $H_{0}: \\mu = 30$." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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zuZKelXSRC9dFgQAQA4JxAf35vEEKmHTTS/NUXc3/ywQAAF8L6zV4zrkpkqbs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\nT9kE4BcBDwAAYD/1bp+mD278hc7Paq0xHy/TCf/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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#here goes your code\n", "\n", "#hint: scipy.stats.poisson.cdf()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Designing a hypothesis test we face a tradeoff between being vulnerable to two possible kinds of error:\n", "1. Type I error: Reject null hypothesis, which was actually true. \n", "2. Type II error: Accept null hypothesis, which was actually false.\n", "\n", "Probability of committing each kind of error is strictly connected with the threshold p-value, which enables us to reject the null hypothesis. This threshold value is often called **significance level**.\n", "\n", "Low significance level reduces the probability of committing type I error, makes it harder to reject false null hypothesis. High significance lowers the criteria for rejecting, which may result in a big number of **false positives**.\n", "\n", "The probability of **not** committing type II error is denoted $\\beta$ and called **power of the test**.\n", "\n", "c) For true lambdas from 31 to 60 and single observation, calculate a power of the test for $H_{0}: \\mu = 30$ and significance level 0.05.\n", "\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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CAPgQCh8AAA7Iyi/Vfe+s1LcbsnRmtwQ9MSZJcQxRBwDUMwofAABu9sOmLN01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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#here goes your code\n", "\n", "#hint: scipy.stats.poisson.isf(), scipy.stats.poisson.cdf()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 2 }