Markov Chain Monte Carlo in Practice

TLDR: The Markov Chain Monte Carlo Implementation Results Summary and Discussion MEDICAL MONITORING Introduction Modelling Medical Monitoring Computing Posterior Distributions Forecasting Model Criticism Illustrative Application Discussion MCMC for NONLINEAR HIERARCHICAL MODELS.

Abstract: INTRODUCING MARKOV CHAIN MONTE CARLO Introduction The Problem Markov Chain Monte Carlo Implementation Discussion HEPATITIS B: A CASE STUDY IN MCMC METHODS Introduction Hepatitis B Immunization Modelling Fitting a Model Using Gibbs Sampling Model Elaboration Conclusion MARKOV CHAIN CONCEPTS RELATED TO SAMPLING ALGORITHMS Markov Chains Rates of Convergence Estimation The Gibbs Sampler and Metropolis-Hastings Algorithm INTRODUCTION TO GENERAL STATE-SPACE MARKOV CHAIN THEORY Introduction Notation and Definitions Irreducibility, Recurrence, and Convergence Harris Recurrence Mixing Rates and Central Limit Theorems Regeneration Discussion FULL CONDITIONAL DISTRIBUTIONS Introduction Deriving Full Conditional Distributions Sampling from Full Conditional Distributions Discussion STRATEGIES FOR IMPROVING MCMC Introduction Reparameterization Random and Adaptive Direction Sampling Modifying the Stationary Distribution Methods Based on Continuous-Time Processes Discussion IMPLEMENTING MCMC Introduction Determining the Number of Iterations Software and Implementation Output Analysis Generic Metropolis Algorithms Discussion INFERENCE AND MONITORING CONVERGENCE Difficulties in Inference from Markov Chain Simulation The Risk of Undiagnosed Slow Convergence Multiple Sequences and Overdispersed Starting Points Monitoring Convergence Using Simulation Output Output Analysis for Inference Output Analysis for Improving Efficiency MODEL DETERMINATION USING SAMPLING-BASED METHODS Introduction Classical Approaches The Bayesian Perspective and the Bayes Factor Alternative Predictive Distributions How to Use Predictive Distributions Computational Issues An Example Discussion HYPOTHESIS TESTING AND MODEL SELECTION Introduction Uses of Bayes Factors Marginal Likelihood Estimation by Importance Sampling Marginal Likelihood Estimation Using Maximum Likelihood Application: How Many Components in a Mixture? Discussion Appendix: S-PLUS Code for the Laplace-Metropolis Estimator MODEL CHECKING AND MODEL IMPROVEMENT Introduction Model Checking Using Posterior Predictive Simulation Model Improvement via Expansion Example: Hierarchical Mixture Modelling of Reaction Times STOCHASTIC SEARCH VARIABLE SELECTION Introduction A Hierarchical Bayesian Model for Variable Selection Searching the Posterior by Gibbs Sampling Extensions Constructing Stock Portfolios With SSVS Discussion BAYESIAN MODEL COMPARISON VIA JUMP DIFFUSIONS Introduction Model Choice Jump-Diffusion Sampling Mixture Deconvolution Object Recognition Variable Selection Change-Point Identification Conclusions ESTIMATION AND OPTIMIZATION OF FUNCTIONS Non-Bayesian Applications of MCMC Monte Carlo Optimization Monte Carlo Likelihood Analysis Normalizing-Constant Families Missing Data Decision Theory Which Sampling Distribution? Importance Sampling Discussion STOCHASTIC EM: METHOD AND APPLICATION Introduction The EM Algorithm The Stochastic EM Algorithm Examples GENERALIZED LINEAR MIXED MODELS Introduction Generalized Linear Models (GLMs) Bayesian Estimation of GLMs Gibbs Sampling for GLMs Generalized Linear Mixed Models (GLMMs) Specification of Random-Effect Distributions Hyperpriors and the Estimation of Hyperparameters Some Examples Discussion HIERARCHICAL LONGITUDINAL MODELLING Introduction Clinical Background Model Detail and MCMC Implementation Results Summary and Discussion MEDICAL MONITORING Introduction Modelling Medical Monitoring Computing Posterior Distributions Forecasting Model Criticism Illustrative Application Discussion MCMC FOR NONLINEAR HIERARCHICAL MODELS Introduction Implementing MCMC Comparison of Strategies A Case Study from Pharmacokinetics-Pharmacodynamics Extensions and Discussion BAYESIAN MAPPING OF DISEASE Introduction Hypotheses and Notation Maximum Likelihood Estimation of Relative Risks Hierarchical Bayesian Model of Relative Risks Empirical Bayes Estimation of Relative Risks Fully Bayesian Estimation of Relative Risks Discussion MCMC IN IMAGE ANALYSIS Introduction The Relevance of MCMC to Image Analysis Image Models at Different Levels Methodological Innovations in MCMC Stimulated by Imaging Discussion MEASUREMENT ERROR Introduction Conditional-Independence Modelling Illustrative examples Discussion GIBBS SAMPLING METHODS IN GENETICS Introduction Standard Methods in Genetics Gibbs Sampling Approaches MCMC Maximum Likelihood Application to a Family Study of Breast Cancer Conclusions MIXTURES OF DISTRIBUTIONS: INFERENCE AND ESTIMATION Introduction The Missing Data Structure Gibbs Sampling Implementation Convergence of the Algorithm Testing for Mixtures Infinite Mixtures and Other Extensions AN ARCHAEOLOGICAL EXAMPLE: RADIOCARBON DATING Introduction Background to Radiocarbon Dating Archaeological Problems and Questions Illustrative Examples Discussion Index