Think Bayes: Bayesian Statistics in Python

✍ Scribed by Downey, Allen B

• Publisher: O'Reilly Media
• Year: 2013
• Tongue: English
• Leaves: 213
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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

✦ Subjects

Science;Mathematics;Computer Science;Computers;Nonfiction;Programming;Coding;Reference;Technical;Textbooks