Think Bayes: Bayesian Statistics in Python

Description

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 Table of Contents Preface My theory, which is mine Modeling and approximation Working with the code Code style Prerequisites Conventions Used in This Book Safari® Books Online How to Contact Us Contributor List Chapter 1. Bayes’s Theorem Conditional probability Conjoint probability The cookie problem Bayes’s theorem The diachronic interpretation The M&M problem The Monty Hall problem Discussion Chapter 2. Computational Statistics Distributions The cookie problem The Bayesian framework The Monty Hall problem Encapsulating the framework The M&M problem Discussion Exercises Chapter 3. Estimation The dice problem The locomotive problem What about that prior? An alternative prior Credible intervals Cumulative distribution functions The German tank problem Discussion Exercises Chapter 4. More Estimation The Euro problem Summarizing the posterior Swamping the priors Optimization The beta distribution Discussion Exercises Chapter 5. Odds and Addends Odds The odds form of Bayes’s theorem Oliver’s blood Addends Maxima Mixtures Discussion Chapter 6. Decision Analysis The Price is Right problem The prior Probability density functions Representing PDFs Modeling the contestants Likelihood Update Optimal bidding Discussion Chapter 7. Prediction The Boston Bruins problem Poisson processes The posteriors The distribution of goals The probability of winning Sudden death Discussion Exercises Chapter 8. Observer Bias The Red Line problem The model Wait times Predicting wait times Estimating the arrival rate Incorporating uncertainty Decision analysis Discussion Exercises Chapter 9. Two Dimensions Paintball The suite Trigonometry Likelihood Joint distributions Conditional distributions Credible intervals Discussion Exercises Chapter 10. Approximate Bayesian Computation The Variability Hypothesis Mean and standard deviation Update The posterior distribution of CV Underflow Log-likelihood A little optimization ABC Robust estimation Who is more variable? Discussion Exercises Chapter 11. Hypothesis Testing Back to the Euro problem Making a fair comparison The triangle prior Discussion Exercises Chapter 12. Evidence Interpreting SAT scores The scale The prior Posterior A better model Calibration Posterior distribution of efficacy Predictive distribution Discussion Chapter 13. Simulation The Kidney Tumor problem A simple model A more general model Implementation Caching the joint distribution Conditional distributions Serial Correlation Discussion Chapter 14. A Hierarchical Model The Geiger counter problem Start simple Make it hierarchical A little optimization Extracting the posteriors Discussion Exercises Chapter 15. Dealing with Dimensions Belly button bacteria Lions and tigers and bears The hierarchical version Random sampling Optimization Collapsing the hierarchy One more problem We’re not done yet The belly button data Predictive distributions Joint posterior Coverage Discussion Index About the Author