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Research in Bayesian analysis and statistical decision theory is rapidly expanding and diversifying, making it increasingly more difficult for any single researcher to stay up to date on all current research frontiers. This book provides a review of current research challenges and opportunities. While the book can not exhaustively cover all current research areas, it does include some exemplary discussion of most research frontiers. Topics include objective Bayesian inference, shrinkage estimation and other decision based estimation, model selection and testing, nonparametric Bayes, the interface of Bayesian and frequentist inference, data mining and machine learning, methods for categorical and spatio-temporal data analysis and posterior simulation methods. Several major application areas are covered: computer models, Bayesian clinical trial design, epidemiology, phylogenetics, bioinformatics, climate modeling and applications in political science, finance and marketing. As a review of current research in Bayesian analysis the book presents a balance between theory and applications. The lack of a clear demarcation between theoretical and applied research is a reflection of the highly interdisciplinary and often applied nature of research in Bayesian statistics. The book is intended as an update for researchers in Bayesian statistics, including non-statisticians who make use of Bayesian inference to address substantive research questions in other fields. It would also be useful for graduate students and research scholars in statistics or biostatistics who wish to acquaint themselves with current research frontiers. Ming-Hui Chen is Professor of Statistics at the University of Connecticut Dipak K. Dey is Head and Professor of Statistics at the University of Connecticut Peter Müller is Professor of Biostatistics at the University of Texas M. D. Anderson Cancer Center Dongchu Sun is Professor of Statistics at the University of Missouri- Columbia and Keying Ye is Professor of Statistics at the University of Texas at San Antonio.
Objective Bayesian inference with applications.
Bayesian decision based estimation and predictive inference.
Bayesian model selection and hypothesis tests.
Bayesian computer models.
Bayesian nonparametrics and semi-parametrics.
Bayesian case influence and frequentist interface.
Bayesian clinical trials.
Bayesian methods for genomics, molecular, and systems biology.
Bayesian data mining and machine learning.
Bayesian inference in political and social sciences, finance, and marketing.
Bayesian categorical data analysis.
Bayesian geophysical, spatial, and temporal statistics.
Posterior simulation and Monte Carlo methods