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11. Bayesian Computational Methods
Christian P. Robert
Subsections
11.1 Introduction
11.2 Bayesian Computational Challenges
11.2.1 Bayesian Point Estimation
11.2.2 Testing Hypotheses
11.2.3 Model Choice
11.3 Monte Carlo Methods
11.3.1 Preamble: Monte Carlo Importance Sampling
11.3.2 First Illustrations
11.3.3 Approximations of the Bayes Factor
11.4 Markov Chain Monte Carlo Methods
11.4.1 Metropolis-Hastings as Universal Simulator
11.4.2 Gibbs Sampling and Latent Variable Models
11.4.3 Reversible Jump Algorithms for Variable Dimension Models
11.5 More Monte Carlo Methods
11.5.1 Adaptivity for MCMC Algorithms
11.5.2 Population Monte Carlo
11.6 Conclusion