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Think Bayes

Book Description

If you know how to program with Python, and know a little about probability, you’re ready to tackle Bayesian statistics. This book shows you how to use Python code instead of math to help you learn Bayesian fundamentals. Once you get the math out of the way, you’ll be able to apply these techniques to real-world problems.

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
  18. Colophon
  19. Copyright