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. Copyright......Page 4 Table of Contents......Page 5 Modeling and approximation......Page 11 Code style......Page 13 Conventions Used in This Book......Page 14 How to Contact Us......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 32 Encapsulating the framework......Page 33 The M&M problem......Page 34 Discussion......Page 35 Exercises......Page 36 The dice problem......Page 37 The locomotive problem......Page 38 What about that prior?......Page 40 An alternative prior......Page 41 Credible intervals......Page 43 Cumulative distribution functions......Page 44 Discussion......Page 45 Exercises......Page 46 The Euro problem......Page 47 Swamping the priors......Page 49 Optimization......Page 51 The beta distribution......Page 52 Discussion......Page 54 Exercises......Page 55 Odds......Page 57 The odds form of Bayes’s theorem......Page 58 Oliver’s blood......Page 59 Addends......Page 60 Maxima......Page 63 Mixtures......Page 65 Discussion......Page 67 The Price is Right problem......Page 69 The prior......Page 70 Representing PDFs......Page 71 Modeling the contestants......Page 73 Update......Page 76 Optimal bidding......Page 77 Discussion......Page 81 The Boston Bruins problem......Page 83 Poisson processes......Page 84 The posteriors......Page 85 The distribution of goals......Page 86 The probability of winning......Page 88 Sudden death......Page 89 Discussion......Page 91 Exercises......Page 92 The model......Page 95 Wait times......Page 97 Predicting wait times......Page 100 Estimating the arrival rate......Page 102 Incorporating uncertainty......Page 104 Decision analysis......Page 105 Discussion......Page 108 Exercises......Page 109 The suite......Page 111 Trigonometry......Page 113 Likelihood......Page 114 Joint distributions......Page 115 Conditional distributions......Page 116 Credible intervals......Page 117 Discussion......Page 120 Exercises......Page 121 The Variability Hypothesis......Page 123 Mean and standard deviation......Page 124 The posterior distribution of CV......Page 126 Underflow......Page 127 A little optimization......Page 129 ABC......Page 131 Robust estimation......Page 132 Who is more variable?......Page 134 Discussion......Page 136 Exercises......Page 137 Back to the Euro problem......Page 139 Making a fair comparison......Page 140 The triangle prior......Page 141 Discussion......Page 142 Exercises......Page 143 Interpreting SAT scores......Page 145 The prior......Page 146 Posterior......Page 148 A better model......Page 150 Calibration......Page 152 Posterior distribution of efficacy......Page 153 Predictive distribution......Page 154 Discussion......Page 155 The Kidney Tumor problem......Page 159 A simple model......Page 161 A more general model......Page 162 Implementation......Page 164 Caching the joint distribution......Page 165 Conditional distributions......Page 166 Serial Correlation......Page 168 Discussion......Page 171 The Geiger counter problem......Page 173 Start simple......Page 174 Make it hierarchical......Page 175 A little optimization......Page 176 Discussion......Page 177 Exercises......Page 178 Belly button bacteria......Page 181 Lions and tigers and bears......Page 182 The hierarchical version......Page 184 Random sampling......Page 186 Optimization......Page 187 Collapsing the hierarchy......Page 188 One more problem......Page 191 We’re not done yet......Page 192 The belly button data......Page 193 Predictive distributions......Page 197 Joint posterior......Page 200 Coverage......Page 202 Discussion......Page 203 Index......Page 205 About the Author......Page 209 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