Applied Bayesian Hierarchical Methods

Emphasizing applications and practical computing aspects, this book presents an up-to-date review of Bayesian hierarchical methods. It provides a complete treatment of the main modeling settings, including meta-analysis, time series, nonlinear regression, and multilevel, multivariate, panel, spatial, and survival data. The text includes realistic worked examples from the social and health sciences, mainly employing the WinBUGS package but also incorporating BayesX code. The author also illustrates MCMC sampling from first principles using R. A set of programs linked to the worked examples is available on www.crcpress.com

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