Think Bayes

Table of contents

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