Author | Chen, Ming-Hui. author |
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Title | Monte Carlo Methods in Bayesian Computation [electronic resource] / by Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2000 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1276-8 |
Descript | XIII, 387 p. online resource |
1 Introduction -- 1.1 Aims -- 1.2 Outline -- 1.3 Motivating Examples -- 1.4 The Bayesian Paradigm -- Exercises -- 2 Markov Chain Monte Carlo Sampling -- 2.1 Gibbs Sampler -- 2.2 Metropolis-Hastings Algorithm -- 2.3 Hit-and-Run Algorithm -- 2.4 Multiple-Try Metropolis Algorithm -- 2.5 Grouping, Collapsing, and Reparameterizations -- 2.6 Acceleration Algorithms for MCMC Sampling -- 2.7 Dynamic Weighting Algorithm -- 2.8 Toward โBlack-Boxโ Sampling -- 2.9 Convergence Diagnostics -- Exercises -- 3 Basic Monte Carlo Methods for Estimating Posterior Quantities -- 3.1 Posterior Quantities -- 3.2 Basic Monte Carlo Methods -- 3.3 Simulation Standard Error Estimation -- 3.4 Improving Monte Carlo Estimates -- 3.5 Controlling Simulation Errors -- Exercises -- 4 Estimating Marginal Posterior Densities -- 4.1 Marginal Posterior Densities -- 4.2 Kernel Methods -- 4.3 IWMDE Methods -- 4.4 Illustrative Examples -- 4.5 Performance Study Using the Kullback-Leibler Divergence -- Exercises -- 5 Estimating Ratios of Normalizing Constants -- 5.1 Introduction -- 5.2 Importance Sampling -- 5.3 Bridge Sampling -- 5.4 Path Sampling -- 5.5 Ratio Importance Sampling -- 5.6 A Theoretical Illustration -- 5.7 Computing Simulation Standard Errors -- 5.8 Extensions to Densities with Different Dimensions -- 5.9 Estimation of Normalizing Constants After Transformation -- 5.10 Other Methods -- 5.11 An Application of Weighted Monte Carlo Estimators -- 5.12 Discussion -- Exercises -- 6 Monte Carlo Methods for Constrained Parameter Problems -- 6.1 Constrained Parameter Problems -- 6.2 Posterior Moments and Marginal Posterior Densities -- 6.3 Computing Normalizing Constants for Bayesian Estimation -- 6.4 Applications -- 6.5 Discussion -- Exercises -- 7 Computing Bayesian Credible and HPD Intervals -- 7.1 Bayesian Credible and HPD Intervals -- 7.2 Estimating Bayesian Credible Intervals -- 7.3 Estimating Bayesian HPD Intervals -- 7.4 Extension to the Constrained Parameter Problems -- 7.5 Numerical Illustration -- 7.6 Discussion -- Exercises -- 8 Bayesian Approaches for Comparing Nonnested Models -- 8.1 Marginal Likelihood Approaches -- 8.2 Scale Mixtures of Multivariate Normal Link Models -- 8.3 โSuper-Modelโ or โSub-Modelโ Approaches -- 8.4 Criterion-Based Methods -- 9 Bayesian Variable Selection -- 9.1 Variable Selection for Logistic Regression Models -- 9.2 Variable Selection for Time Series Count Data Models -- 9.3 Stochastic Search Variable Selection -- 9.4 Bayesian Model Averaging -- 9.5 Reversible Jump MCMC Algorithm for Variable Selection -- Exercises -- 10 Other Topics -- 10.1 Bayesian Model Adequacy -- 10.2 Computing Posterior Modes -- 10.3 Bayesian Computation for Proportional Hazards Models -- 10.4 Posterior Sampling for Mixture of Dirichlet Process Models -- Exercises -- References -- Author Index