Chapter 2 Basics of Markov Chain Monte Carlo

Note: This chapter is still under construction. The corresponding slides are available here and here.

2.1 Motivation

  • Deterministic integration.

  • Monte Carlo.

  • Markov chain Monte Carlo.

2.2 Gibbs Sampler

  • Algorithm summary.

  • Example: Bivariate Normal.

2.3 Metropolis-Hastings Algorithm

  • Algorithm summary.

  • Common transition densities.

  • Why does it work?

2.4 Example: Weibull Distribution

  • MCMC diagnostics.

  • Marginalizing variables.

2.5 Adaptive Metropolis-within-Gibbs

2.6 Example: Noncentral-t Distribution

  • Bayesian Data Augmentation.

  • Code Checking.

2.7 Computational Resources