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3. Markov Chain
Monte Carlo Technology
Siddhartha Chib
Subsections
3.1 Introduction
3.1.1 Organization
3.2 Markov Chains
3.2.1 Definitions and Results
3.2.2 Computation of Numerical Accuracy and Inefficiency Factor
3.3 Metropolis-Hastings Algorithm
3.3.1 Convergence Results
3.3.2 Example
3.3.2.1 Random Walk Proposal Density
3.3.2.2 Tailored Proposal Density
3.3.3 Multiple-Block M-H Algorithm
3.4 The Gibbs Sampling Algorithm
3.4.1 The Algorithm
3.4.2 Invariance of the Gibbs Markov Chain
3.4.3 Sufficient Conditions for Convergence
3.4.4 Example: Simulating a Truncated Multivariate Normal
3.5 MCMC Sampling with Latent Variables
3.6 Estimation of Density Ordinates
3.7 Sampler Performance and Diagnostics
3.8 Strategies for Improving Mixing
3.8.1 Choice of Blocking
3.8.2 Tuning the Proposal Density
3.8.3 Other Strategies
3.9 Concluding Remarks