Applied Bayesian Hierarchical Methods

Applied Bayesian Hierarchical Methods

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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.
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Product details

  • Electronic book text | 604 pages
  • Chapman & Hall/CRC
  • London, United Kingdom
  • English
  • Approx 800 equations; 15 Tables, black and white; 43 Illustrations, black and white
  • 1584887214
  • 9781584887218

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
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Review quote

"...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
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About Peter D. Congdon

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.
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