Applied Bayesian Hierarchical Methods: 1st Edition (Hardback) book cover

Applied Bayesian Hierarchical Methods

1st Edition

By Peter D. Congdon

Chapman and Hall/CRC

604 pages | 43 B/W Illus.

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pub: 2010-05-19
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Description

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.

Reviews

"…excellent … for learning or applying [the Bayesian approach]. … an excellent place for readers to learn and practice Bayesian concepts."

Journal of Statistical Computation and Simulation, Vol. 84, 2014

"The overall presentation of concepts is logical and supported by detailed mathematical descriptions. … the text provides a great reference for the underlying formalities of all of the methods discussed. Throughout each chapter, the author highlights methodological issues in relation to the topics presented with references to the literature, displaying his comprehensive and up-to-date knowledge of the material. The emphasis placed on computational issues related to the implementation of MCMC routines for model fitting (with BUGS code provided at the end of each chapter) is welcome, as this issue has the potential to cause a lot of headaches for practitioners trying to employ Bayesian methods. … a comprehensive and valuable resource."

—Kris M. Jamsen and Lyle C. Gurrin, Australian and New Zealand Journal of Statistics, 2012

"… a good reference for applied work in biometrics. It makes it easy to analyze models with the same type of data structures that are described in the book by supplying the companion code."

—Wolfgang Polasek, Statistical Papers, August 2012

"Many of the hierarchical modeling techniques in this book are recently proposed and new in the literature. The author provides very comprehensive references … . Even though many examples are related to health and social science, they also would be helpful to users in engineering and other fields. … In summary, the book presents many excellent Bayesian hierarchical modeling techniques to tackle difficult and realistic modeling issues that many researchers may encounter in their scientific areas. … an excellent collection and reference for researchers who are interested in applying the most recent Bayesian hierarchical modeling methods to their own areas."

—Zhaojun (Steven) Li, Journal of Quality Technology, Vol. 43, No. 4, October 2011

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

About the Author

Peter D. Congdon is a research professor of quantitative geography and health statistics in the Centre for Statistics and Department of Geography at the University of London, UK.

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General