Applied Bayesian Hierarchical Methods

The use of Markov chain Monte Carlo (MCMC) methods for estimating hierarchical models involves complex data structures and is often described as a revolutionary development. An intermediate-level treatment of Bayesian hierarchical models and their applications, Applied Bayesian Hierarchical Methods demonstrates the advantages of a Bayesian approach to data sets involving inferences for collections of related units or variables and in methods where parameters can be treated as random collections. Emphasizing computational issues, the book provides examples of the following application settings: meta-analysis, data structured in space or time, multilevel and longitudinal data, multivariate data, nonlinear regression, and survival time data. For the worked examples, the text mainly employs the WinBUGS package, allowing readers to explore alternative likelihood assumptions, regression structures, and assumptions on prior densities. It also incorporates BayesX code, which is particularly useful in nonlinear regression. To demonstrate MCMC sampling from first principles, the author includes worked examples using the R package. Through illustrative data analysis and attention to statistical computing, this book focuses on the practical implementation of Bayesian hierarchical methods. It also discusses several issues that arise when applying Bayesian techniques in hierarchical and random effects models.

Table of Contents:
Bayesian Methods for Complex Data: Estimation and Inference Introduction Posterior Inference from Bayes Formula Markov Chain Sampling in Relation to Monte Carlo Methods: Obtaining Posterior Inferences Hierarchical Bayes Applications Metropolis Sampling Choice of Proposal Density Obtaining Full Conditional Densities Metropolis–Hastings Sampling Gibbs Sampling Assessing Efficiency and Convergence: Ways of Improving Convergence Choice of Prior Density Model Fit, Comparison, and Checking Introduction Formal Methods: Approximating Marginal Likelihoods Effective Model Dimension and Deviance Information Criterion Variance Component Choice and Model Averaging Predictive Methods for Model Choice and Checking Estimating Posterior Model Probabilities Hierarchical Estimation for Exchangeable Units: Continuous and Discrete Mixture Approaches Introduction Hierarchical Priors for Ensemble Estimation using Continuous Mixtures The Normal-Normal Hierarchical Model and Its Applications Priors for Second Stage Variance Parameters Multivariate Meta-Analysis Heterogeneity in Count Data: Hierarchical Poisson Models Binomial and Multinomial Heterogeneity Discrete Mixtures and Nonparametric Smoothing Methods Nonparametric Mixing via Dirichlet Process and Polya Tree Priors Structured Priors Recognizing Similarity over Time and Space Introduction Modeling Temporal Structure: Autoregressive Models State Space Priors for Metric Data Time Series for Discrete Responses: State Space Priors and Alternatives Stochastic Variances Modeling Discontinuities in Time Spatial Smoothing and Prediction for Area Data Conditional Autoregressive Priors Priors on Variances in Conditional Spatial Models Spatial Discontinuity and Robust Smoothing Models for Point Processes Regression Techniques using Hierarchical Priors Introduction Regression for Overdispersed Discrete Data Latent Scales for Binary and Categorical Data Nonconstant Regression Relationships and Variance Heterogeneity Heterogeneous Regression and Discrete Mixture Regressions Time Series Regression: Correlated Errors and Time-Varying Regression Effects Spatial Correlation in Regression Residuals Spatially Varying Regression Effects: Geographically Weighted Linear Regression and Bayesian Spatially Varying Coefficient Models Bayesian Multilevel Models Introduction The Normal Linear Mixed Model for Hierarchical Data Discrete Responses: General Linear Mixed Model, Conjugate, and Augmented Data Models Crossed and Multiple Membership Random Effects Robust Multilevel Models Multivariate Priors, with a Focus on Factor and Structural Equation Models Introduction The Normal Linear SEM and Factor Models Identifiability and Priors on Loadings Multivariate Exponential Family Outcomes and General Linear Factor Models Robust Options in Multivariate and Factor Analysis Multivariate Spatial Priors for Discrete Area Frameworks Spatial Factor Models Multivariate Time Series Hierarchical Models for Panel Data Introduction General Linear Mixed Models for Panel Data Temporal Correlation and Autocorrelated Residuals Categorical Choice Panel Data Observation-Driven Autocorrelation: Dynamic Panel Models Robust Panel Models: Heteroscedasticity, Generalized Error Densities, and Discrete Mixtures Multilevel, Multivariate, and Multiple Time Scale Longitudinal Data Missing Data in Panel Models Survival and Event History Models Introduction Survival Analysis in Continuous Time Semiparametric Hazards Including Frailty Discrete Time Hazard Models Dependent Survival Times: Multivariate and Nested Survival Times Competing Risks Hierarchical Methods for Nonlinear Regression Introduction Nonparametric Basis Function Models for the Regression Mean Multivariate Basis Function Regression Heteroscedasticity via Adaptive Nonparametric Regression General Additive Methods Nonparametric Regression Methods for Longitudinal Analysis Appendix: Using WinBUGS and BayesX References Index