Markov Chain Monte Carlo in Practice

INTRODUCING MARKOV CHAIN MONTE CARLOIntroductionThe ProblemMarkov Chain Monte CarloImplementationDiscussion HEPATITIS B: A CASE STUDY IN MCMC METHODSIntroductionHepatitis B ImmunizationModellingFitting a Model Using Gibbs SamplingModel ElaborationConclusionMARKOV CHAIN CONCEPTS RELATED TO SAMPLING ALGORITHMSMarkov ChainsRates of ConvergenceEstimationThe Gibbs Sampler and Metropolis-Hastings Algorithm INTRODUCTION TO GENERAL STATE-SPACE MARKOV CHAIN THEORY IntroductionNotation and DefinitionsIrreducibility, Recurrence, and ConvergenceHarris RecurrenceMixing Rates and Central Limit TheoremsRegenerationDiscussionFULL CONDITIONAL DISTRIBUTIONSIntroductionDeriving Full Conditional DistributionsSampling from Full Conditional DistributionsDiscussionSTRATEGIES FOR IMPROVING MCMCIntroductionReparameterizationRandom and Adaptive Direction SamplingModifying the Stationary DistributionMethods Based on Continuous-Time ProcessesDiscussionIMPLEMENTING MCMCIntroductionDetermining the Number of IterationsSoftware and ImplementationOutput AnalysisGeneric Metropolis AlgorithmsDiscussionINFERENCE AND MONITORING CONVERGENCEDifficulties in Inference from Markov Chain SimulationThe Risk of Undiagnosed Slow ConvergenceMultiple Sequences and Overdispersed Starting PointsMonitoring Convergence Using Simulation OutputOutput Analysis for InferenceOutput Analysis for Improving EfficiencyMODEL DETERMINATION USING SAMPLING-BASED METHODSIntroductionClassical ApproachesThe Bayesian Perspective and the Bayes FactorAlternative Predictive DistributionsHow to Use Predictive DistributionsComputational IssuesAn ExampleDiscussionHYPOTHESIS TESTING AND MODEL SELECTIONIntroductionUses of Bayes FactorsMarginal Likelihood Estimation by Importance SamplingMarginal Likelihood Estimation Using Maximum LikelihoodApplication: How Many Components in a Mixture?DiscussionAppendix: S-PLUS Code for the Laplace-Metropolis EstimatorMODEL CHECKING AND MODEL IMPROVEMENTIntroductionModel Checking Using Posterior Predictive SimulationModel Improvement via ExpansionExample: Hierarchical Mixture Modelling of Reaction TimesSTOCHASTIC SEARCH VARIABLE SELECTIONIntroductionA Hierarchical Bayesian Model for Variable SelectionSearching the Posterior by Gibbs SamplingExtensionsConstructing Stock Portfolios With SSVSDiscussionBAYESIAN MODEL COMPARISON VIA JUMP DIFFUSIONSIntroductionModel ChoiceJump-Diffusion SamplingMixture DeconvolutionObject RecognitionVariable SelectionChange-Point IdentificationConclusionsESTIMATION AND OPTIMIZATION OF FUNCTIONSNon-Bayesian Applications of MCMCMonte Carlo OptimizationMonte Carlo Likelihood AnalysisNormalizing-Constant FamiliesMissing DataDecision TheoryWhich Sampling Distribution?Importance SamplingDiscussionSTOCHASTIC EM: METHOD AND APPLICATIONIntroductionThe EM AlgorithmThe Stochastic EM AlgorithmExamplesGENERALIZED LINEAR MIXED MODELSIntroductionGeneralized Linear Models (GLMs)Bayesian Estimation of GLMsGibbs Sampling for GLMsGeneralized Linear Mixed Models (GLMMs)Specification of Random-Effect DistributionsHyperpriors and the Estimation of HyperparametersSome ExamplesDiscussionHIERARCHICAL LONGITUDINAL MODELLINGIntroductionClinical BackgroundModel Detail and MCMC ImplementationResultsSummary and DiscussionMEDICAL MONITORINGIntroductionModelling Medical MonitoringComputing Posterior DistributionsForecastingModel CriticismIllustrative ApplicationDiscussionMCMC FOR NONLINEAR HIERARCHICAL MODELSIntroductionImplementing MCMCComparison of StrategiesA Case Study from Pharmacokinetics-PharmacodynamicsExtensions and DiscussionBAYESIAN MAPPING OF DISEASEIntroductionHypotheses and NotationMaximum Likelihood Estimation of Relative RisksHierarchical Bayesian Model of Relative RisksEmpirical Bayes Estimation of Relative RisksFully Bayesian Estimation of Relative RisksDiscussionMCMC IN IMAGE ANALYSISIntroductionThe Relevance of MCMC to Image AnalysisImage Models at Different LevelsMethodological Innovations in MCMC Stimulated by ImagingDiscussionMEASUREMENT ERRORIntro