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Presents an introduction to the methods of simulation technique. This second edition includes a discussion of computation using both R and WinBUGS; and additional exercises and selected solutions within the text, with all data sets and software. It is aimed at those working with MCMC techniques, especially research and graduate statisticians.
INTRODUCTIONSTOCHASTIC SIMULATIONIntroductionGeneration of Discrete Random QuantitiesGeneration of Continuous Random QuantitiesGeneration of Random Vectors and MatricesResampling MethodsExercisesBAYESIAN INFERENCEIntroductionBayes' TheoremConjugate DistributionsHierarchical ModelsDynamic ModelsSpatial ModelsModel ComparisonExercisesAPPROXIMATE METHODS OF INFERENCEIntroductionAsymptotic ApproximationsApproximations by Gaussian QuadratureMonte Carlo IntegrationMethods Based on Stochastic SimulationExercisesMARKOV CHAINSIntroductionDefinition and Transition ProbabilitiesDecomposition of the State SpaceStationary DistributionsLimiting TheoremsReversible ChainsContinuous State SpacesSimulation of a Markov ChainData Augmentation or Substitution SamplingExercisesGIBBS SAMPLINGIntroductionDefinition and PropertiesImplementation and OptimizationConvergence DiagnosticsApplicationsMCMC-Based Software for Bayesian ModelingAppendix 5.A: BUGS Code for Example 5.7Appendix 5.B: BUGS Code for Example 5.8ExercisesMETROPOLIS-HASTINGS ALGORITHMSIntroductionDefinition and PropertiesSpecial CasesHybrid AlgorithmsApplicationsExercisesFURTHER TOPICS IN MCMCIntroductionModel AdequacyModel Choice: MCMC Over Model and Parameter SpacesConvergence AccelerationExercisesReferencesAuthor IndexSubject Index