Think Bayes by Downey, Allen B. -- Read -- Imperial Library of Trantor

Index

Think Bayes 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

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

2. Computational Statistics

Distributions The cookie problem The Bayesian framework The Monty Hall problem Encapsulating the framework The M&M problem Discussion Exercises

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

4. More Estimation

The Euro problem Summarizing the posterior Swamping the priors Optimization The beta distribution Discussion Exercises

5. Odds and Addends

Odds The odds form of Bayes’s theorem Oliver’s blood Addends Maxima Mixtures Discussion

6. Decision Analysis

The Price is Right problem The prior Probability density functions Representing PDFs Modeling the contestants Likelihood Update Optimal bidding Discussion

7. Prediction

The Boston Bruins problem Poisson processes The posteriors The distribution of goals The probability of winning Sudden death Discussion Exercises

8. Observer Bias

The Red Line problem The model Wait times Predicting wait times Estimating the arrival rate Incorporating uncertainty Decision analysis Discussion Exercises

9. Two Dimensions

Paintball The suite Trigonometry Likelihood Joint distributions Conditional distributions Credible intervals Discussion Exercises

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

11. Hypothesis Testing

Back to the Euro problem Making a fair comparison The triangle prior Discussion Exercises

12. Evidence

Interpreting SAT scores The scale The prior Posterior A better model Calibration Posterior distribution of efficacy Predictive distribution Discussion

13. Simulation

The Kidney Tumor problem A simple model A more general model Implementation Caching the joint distribution Conditional distributions Serial Correlation Discussion

14. A Hierarchical Model

The Geiger counter problem Start simple Make it hierarchical A little optimization Extracting the posteriors Discussion Exercises

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 Colophon Copyright