Applied Bayesian Hierarchical Methods

1. Auflage 2010
ISBN: 978-1-58488-720-1
Verlag: Chapman and Hall/CRC

Buch, Englisch, 604 Seiten, Format (B × H): 156 mm x 235 mm, Gewicht: 975 g

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.

Zielgruppe

Researchers, practitioners, and graduate students in statistics, biostatistics, and the health and social sciences.

Autoren/Hrsg.

Congdon, Peter D.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

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 ConvergenceChoice of Prior Density

Model Fit, Comparison, and Checking Introduction Formal Methods: Approximating Marginal LikelihoodsEffective Model Dimension and Deviance Information CriterionVariance Component Choice and Model Averaging Predictive Methods for Model Choice and CheckingEstimating Posterior Model Probabilities
Hierarchical Estimation for Exchangeable Units: Continuous and Discrete Mixture ApproachesIntroduction Hierarchical Priors for Ensemble Estimation using Continuous Mixtures The Normal-Normal Hierarchical Model and Its Applications Priors for Second Stage Variance ParametersMultivariate Meta-Analysis Heterogeneity in Count Data: Hierarchical Poisson ModelsBinomial and Multinomial HeterogeneityDiscrete Mixtures and Nonparametric Smoothing MethodsNonparametric Mixing via Dirichlet Process and Polya Tree Priors
Structured Priors Recognizing Similarity over Time and SpaceIntroductionModeling Temporal Structure: Autoregressive ModelsState Space Priors for Metric DataTime Series for Discrete Responses: State Space Priors and AlternativesStochastic Variances Modeling Discontinuities in Time Spatial Smoothing and Prediction for Area Data Conditional Autoregressive PriorsPriors on Variances in Conditional Spatial Models Spatial Discontinuity and Robust Smoothing Models for Point Processes
Regression Techniques using Hierarchical PriorsIntroduction 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 ResidualsSpatially 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 ModelsCrossed and Multiple Membership Random EffectsRobust Multilevel Models
Multivariate Priors, with a Focus on Factor and Structural Equation ModelsIntroduction The Normal Linear SEM and Factor ModelsIdentifiability and Priors on LoadingsMultivariate Exponential Family Outcomes and General Linear Factor ModelsRobust Options in Multivariate and Factor AnalysisMultivariate Spatial Priors for Discrete Area Frameworks Spatial Factor Models Multivariate Time Series
Hierarchical Models for Panel DataIntroduction General Linear Mixed Models for Panel DataTemporal Correlation and Autocorrelated ResidualsCategorical Choice Panel Data Observation-Driven Autocorrelation: Dynamic Panel ModelsRobust Panel Models: Heteroscedasticity, Generalized Error Densities, and Discrete MixturesMultilevel, Multivariate, and Multiple Time Scale Longitudinal DataMissing Data in Panel Models
Survival and Event History ModelsIntroduction Survival Analysis in Continuous Time Semiparametric Hazards Including Frailty Discrete Time Hazard Models Dependent Survival Times: Multivariate and Nested Survival TimesCompeting Risks

Hierarchical Methods for Nonlinear RegressionIntroduction Nonparametric Basis Function Models for the Regression MeanMultivariate Basis Function Regression Heteroscedasticity via Adaptive Nonparametric Regression General Additive Methods Nonparametric Regression Methods for Longitudinal Analysis

Appendix: Using WinBUGS and BayesX
References
Index

Über Autor(innen)

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.