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.
Author(s): Allen Downey B.
Publisher: O'Reilly Media
Year: 2013
Language: English
Pages: 210
Tags: Библиотека;Компьютерная литература;Python;
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
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