Think Bayes : Bayesian Statistics in Python

If you know how to program with Python and also know a little about probability, you’re ready to tackle Bayesian statistics. With this book, you'll learn how to solve statistical problems with Python code instead of mathematical notation, and use discrete probability distributions instead of continuous mathematics. Once you get the math out of the way, the Bayesian fundamentals will become clearer, and you’ll begin to apply these techniques to real-world problems. Bayesian statistical methods are becoming more common and more important, but not many resources are available to help beginners. Based on undergraduate classes taught by author Allen Downey, this book’s computational approach helps you get a solid start. * Use your existing programming skills to learn and understand Bayesian statistics * Work with problems involving estimation, prediction, decision analysis, evidence, and hypothesis testing * Get started with simple examples, using coins, M&Ms, Dungeons & Dragons dice, paintball, and hockey * Learn computational methods for solving real-world problems, such as interpreting SAT scores, simulating kidney tumors, and modeling the human microbiome. Cover......Page 1 Copyright......Page 4 Table of Contents......Page 5 Modeling and approximation......Page 11 Working with the code......Page 13 Prerequisites......Page 14 Safari® Books Online......Page 15 Contributor List......Page 16 Conditional probability......Page 19 Conjoint probability......Page 20 Bayes’s theorem......Page 21 The diachronic interpretation......Page 23 The M&M problem......Page 24 The Monty Hall problem......Page 25 Discussion......Page 27 Distributions......Page 29 The cookie problem......Page 30 The Bayesian framework......Page 31 The Monty Hall problem......Page 33 The M&M problem......Page 34 Exercises......Page 36 The dice problem......Page 37 The locomotive problem......Page 38 What about that prior?......Page 41 An alternative prior......Page 42 Cumulative distribution functions......Page 44 The German tank problem......Page 45 Exercises......Page 46 The Euro problem......Page 49 Swamping the priors......Page 51 Optimization......Page 53 The beta distribution......Page 55 Discussion......Page 56 Exercises......Page 57 Odds......Page 59 The odds form of Bayes’s theorem......Page 60 Oliver’s blood......Page 61 Addends......Page 62 Maxima......Page 65 Mixtures......Page 68 Discussion......Page 70 The Price is Right problem......Page 71 The prior......Page 72 Representing PDFs......Page 73 Modeling the contestants......Page 76 Likelihood......Page 78 Update......Page 79 Optimal bidding......Page 80 Discussion......Page 83 The Boston Bruins problem......Page 85 Poisson processes......Page 86 The posteriors......Page 87 The distribution of goals......Page 88 The probability of winning......Page 90 Sudden death......Page 91 Discussion......Page 93 Exercises......Page 94 The model......Page 97 Wait times......Page 99 Predicting wait times......Page 102 Estimating the arrival rate......Page 105 Incorporating uncertainty......Page 107 Decision analysis......Page 109 Discussion......Page 111 Exercises......Page 112 Paintball......Page 113 The suite......Page 114 Trigonometry......Page 115 Likelihood......Page 117 Joint distributions......Page 118 Conditional distributions......Page 119 Credible intervals......Page 120 Discussion......Page 122 Exercises......Page 123 The Variability Hypothesis......Page 125 Mean and standard deviation......Page 126 The posterior distribution of CV......Page 128 Underflow......Page 129 A little optimization......Page 131 ABC......Page 133 Robust estimation......Page 134 Who is more variable?......Page 136 Exercises......Page 139 Back to the Euro problem......Page 141 Making a fair comparison......Page 142 Discussion......Page 144 Exercises......Page 145 Interpreting SAT scores......Page 147 The prior......Page 148 Posterior......Page 150 A better model......Page 152 Calibration......Page 154 Posterior distribution of efficacy......Page 155 Predictive distribution......Page 157 Discussion......Page 158 The Kidney Tumor problem......Page 161 A simple model......Page 163 A more general model......Page 164 Implementation......Page 166 Caching the joint distribution......Page 167 Conditional distributions......Page 168 Serial Correlation......Page 170 Discussion......Page 173 The Geiger counter problem......Page 175 Start simple......Page 176 Make it hierarchical......Page 177 A little optimization......Page 178 Extracting the posteriors......Page 179 Discussion......Page 180 Exercises......Page 181 Belly button bacteria......Page 183 Lions and tigers and bears......Page 184 The hierarchical version......Page 186 Random sampling......Page 188 Collapsing the hierarchy......Page 190 One more problem......Page 193 We’re not done yet......Page 194 The belly button data......Page 196 Predictive distributions......Page 199 Joint posterior......Page 203 Coverage......Page 204 Discussion......Page 206 Index......Page 209 Colophon......Page 213 If you know how to program with Python and also know a little about probability, you’re ready to tackle Bayesian statistics. With this book, you'll learn how to solve statistical problems with Python code instead of mathematical notation, and use discrete probability distributions instead of continuous mathematics. Once you get the math out of the way, the Bayesian fundamentals will become clearer, and you’ll begin to apply these techniques to real-world problems.Bayesian statistical methods are becoming more common and more important, but not many resources are available to help beginners. Based on undergraduate classes taught by author Allen Downey, this book’s computational approach helps you get a solid start.Use your existing programming skills to learn and understand Bayesian statisticsWork with problems involving estimation, prediction, decision analysis, evidence, and hypothesis testingGet started with simple examples, using coins, M&Ms, Dungeons & Dragons dice, paintball, and hockeyLearn computational methods for solving real-world problems, such as interpreting SAT scores, simulating kidney tumors, and modeling the human microbiome. Annotation If you know how to program with Python and also know a little about probability, youre ready to tackle Bayesian statistics. With this book, you'll learn how to solve statistical problems with Python code instead of mathematical notation, and use discrete probability distributions instead of continuous mathematics. Once you get the math out of the way, the Bayesian fundamentals will become clearer, and youll begin to apply these techniques to real-world problems. Bayesian statistical methods are becoming more common and more important, but not many resources are available to help beginners. Based on undergraduate classes taught by author Allen Downey, this books computational approach helps you get a solid start. Use your existing programming skills to learn and understand Bayesian statisticsWork with problems involving estimation, prediction, decision analysis, evidence, and hypothesis testingGet started with simple examples, using coins, M & Ms, Dungeons & Dragons dice, paintball, and hockeyLearn computational methods for solving real-world problems, such as interpreting SAT scores, simulating kidney tumors, and modeling the human microbiome Think Bayes is an introduction to Bayesian statistics using computational methods. The premise of this book, and the other books in the Think X series, is that if you know how to program, you can use that skill to learn other topics. Most books on Bayesian statistics use mathematical notation and present ideas in terms of mathematical concepts like calculus. This book uses Python code instead of math, and discrete approximations instead of continuous mathematics. As a result, what would be an integral in a math book becomes a summation, and most operations on probability distributions are simple loops. I think this presentation is easier to understand, at least for people with programming skills. It is also more general, because when we make modeling decisions, we can choose the most appropriate model without worrying too much about whether the model lends itself to conventional analysis. Also, it provides a smooth development path from simple examples to real-world problems Printing History September, 2013: First Edition 2013-09-10: First release 2014-02-10: Second release 2014-08-22: Third release 2016-06-03: Fourth release