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. Probability distributions
2. Probability and Bayes Rule
3. Conjugate priors 1
4. Conjugate priors 2
5. Objective priors
6. Gibbs sampling
7. Metropolis sampling
8. MCMC convergence diagnostics
9. Linear regression
10. Generalized linear mixed models
11. Bayes factors
12. Model selection
13. Hierarchical models