Notes

• Introduction
• Probability and Bayes Theorem (Probability, Bayes’ Theorem, HIV example)
• Basics of Bayesian inference (Introduction, Summarizing a posterior, Predictions)
• Selecting priors (Conjugate Priors, Objective Bayes)
• Bayesian computing (Deterministic, MCMC, Convergence)
• Linear models (Linear models, Advanced models)
• Model comparisons (Comparisons)
• Hierarchical models (Hierarchical models)
• Frequentist properties of Bayesian methods (Properties)

Derivations for all sections

Lab summaries

1. MLK Day
2. Probability and Bayes Rule
3. Summarizing a posterior distribution
4. Conjugate priors
5. Objective Bayes priors
6. Gibbs sampling
7. Metropolis sampling
8. MCMC convergence diagnostics
9. Linear regression
10. Advanced models
11. Model selection
12. Model selection criteria
13. Hierarchical models