Think Bayes

by Allen B. Downey

Overview

If you know how to program, you're ready to tackle Bayesian statistics. With this book, you'll learn how to solve statistical problems with Python code instead of mathematical formulas, using discrete probability distributions rather than 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 there aren't many resources available to help beginners. Based on undergraduate classes taught by author Allen B. Downey, this book's computational approach helps you get a solid start.

• Use your programming skills to learn and understand Bayesian statistics
• Work with problems involving estimation, prediction, decision analysis, evidence, and Bayesian hypothesis testing
• Get started with simple examples, using coins, dice, and a bowl of cookies
• Learn computational methods for solving real-world problems

Product Details

ISBN-13:	9781492089414
Publisher:	O'Reilly Media, Incorporated
Publication date:	05/18/2021
Sold by:	Barnes & Noble
Format:	eBook
Pages:	338
File size:	8 MB

About the Author

Allen Downey is a Professor of Computer Science at Olin College of Engineering. He has taught computer science at Wellesley College, Colby College and U.C. Berkeley. He has a Ph.D. in Computer Science from U.C. Berkeley and Master’s and Bachelor’s degrees from MIT. He is the author of Think Python, Think Bayes, Think DSP, and a blog, Probably Overthinking It.

Table of Contents

Preface ix

1 Bayes's Theorem 1

Conditional probability 1

Conjoint probability 2

The cookie problem 3

Bayes's theorem 3

The diachronic interpretation 5

The M&M problem 6

The Monty Hall problem 7

Discussion 9

2 Computational Statistics 11

Distributions 11

The cookie problem 12

The Bayesian framework 13

The Monty Hall problem 14

Encapsulating the framework 15

The M&M problem 16

Discussion 17

Exercises 18

3 Estimation 19

The dice problem 19

The locomotive problem 20

What about that prior? 22

An alternative prior 23

Credible intervals 25

Cumulative distribution functions 26

The German tank problem 27

Discussion 27

Exercises 28

4 More Estimation 29

The Euro problem 29

Summarizing the posterior 31

Swamping the priors 31

Optimization 33

The beta distribution 34

Discussion 36

Exercises 37

5 Odds and Addends 39

Odds 39

The odds form of Bayes's theorem 40

Oliver's blood 41

Addends 42

Maxima 45

Mixtures 47

Discussion 49

6 Decision Analysis 51

The Price is Right problem 51

The prior 52

Probability density functions 53

Representing PDFs 53

Modeling the contestants 55

Likelihood 58

Update 58

Optimal bidding 59

Discussion 63

7 Prediction 65

The Boston Bruins problem 65

Poisson processes 66

The posteriors 67

The distribution of goals 68

The probability of winning 70

Sudden death 71

Discussion 73

Exercises 74

8 Observer Bias 77

The Red Line problem 77

The model 77

Wait times 79

Predicting wait times 82

Estimating the arrival rate 84

Incorporating uncertainty 86

Decision analysis 87

Discussion 90

Exercises 91

9 Two Dimensions 93

Paintball 93

The suite 93

Trigonometry 95

Likelihood 96

Joint distributions 97

Conditional distributions 98

Credible intervals 99

Discussion 102

Exercises 103

10 Approximate Bayesian Computation 105

The Variability Hypothesis 105

Mean and standard deviation 106

Update 108

The posterior distribution of CV 108

Underflow 109

Log-likelihood 111

A little optimization 111

ABC 113

Robust estimation 114

Who is more variable? 116

Discussion 118

Exercises 119

11 Hypothesis Testing 121

Back to the Euro problem 121

Making a fair comparison 122

The triangle prior 123

Discussion 124

Exercises 125

12 Evidence 127

Interpreting SAT scores 127

The scale 128

The prior 128

Posterior 130

A better model 132

Calibration 134

Posterior distribution of efficacy 135

Predictive distribution 136

Discussion 137

13 Simulation 141

The Kidney Tumor problem 141

A simple model 143

A more general model 144

Implementation 146

Caching the joint distribution 147

Conditional distributions 148

Serial Correlation 150

Discussion 153

14 A Hierarchical Model 155

The Geiger counter problem 155

Start simple 156

Make it hierarchical 157

A little optimization 158

Extracting the posteriors 159

Discussion 159

Exercises 160

15 Dealing with Dimensions 163

Belly button bacteria 163

Lions and tigers and bears 164

The hierarchical version 166

Random sampling 168

Optimization 169

Collapsing the hierarchy 170

One more problem 173

We're not done yet 174

The belly button data 175

Predictive distributions 179

Joint posterior 182

Coverage 184

Discussion 185

Index 187