Think Bayes: Bayesian Statistics Made Simple

Allen B. Downey

Version 1.0.9

Copyright 2012 Allen B. Downey

Permission is granted to copy, distribute, and/or modify this document under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International Unported License, which is available at http://creativecommons.org/licenses/by-nc-sa/4.0/.

• Preface
  • My theory, which is mine
  • Modeling and approximation
  • Working with the code
  • Code style
  • Prerequisites
  • Contributor List
• 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
• Computational Statistics
  • Distributions
  • The cookie problem
  • The Bayesian framework
  • The Monty Hall problem
  • Encapsulating the framework
  • The M&M problem
  • Discussion
  • Exercises
• 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
• More Estimation
  • The Euro problem
  • Summarizing the posterior
  • Swamping the priors
  • Optimization
  • The beta distribution
  • Discussion
  • Exercises
• Odds and Addends
  • Odds
  • The odds form of Bayes’s theorem
  • Oliver’s blood
  • Addends
  • Maxima
  • Mixtures
  • Discussion
• Decision Analysis
  • The Price is Right problem
  • The prior
  • Probability density functions
  • Representing PDFs
  • Modeling the contestants
  • Likelihood
  • Update
  • Optimal bidding
  • Discussion
• Prediction
  • The Boston Bruins problem
  • Poisson processes
  • The posteriors
  • The distribution of goals
  • The probability of winning
  • Sudden death
  • Discussion
  • Exercises
• Observer Bias
  • The Red Line problem
  • The model
  • Wait times
  • Predicting wait times
  • Estimating the arrival rate
  • Incorporating uncertainty
  • Decision analysis
  • Discussion
  • Exercises
• Two Dimensions
  • Paintball
  • The suite
  • Trigonometry
  • Likelihood
  • Joint distributions
  • Conditional distributions
  • Credible intervals
  • Discussion
  • Exercises
• 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
• Hypothesis Testing
  • Back to the Euro problem
  • Making a fair comparison
  • The triangle prior
  • Discussion
  • Exercises
• Evidence
  • Interpreting SAT scores
  • The scale
  • The prior
  • Posterior
  • A better model
  • Calibration
  • Posterior distribution of efficacy
  • Predictive distribution
  • Discussion
• Simulation
  • The Kidney Tumor problem
  • A simple model
  • A more general model
  • Implementation
  • Caching the joint distribution
  • Conditional distributions
  • Serial Correlation
  • Discussion
• A Hierarchical Model
  • The Geiger counter problem
  • Start simple
  • Make it hierarchical
  • A little optimization
  • Extracting the posteriors
  • Discussion
  • Exercises
• 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

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