Bayesian Theory and Applications

The development of hierarchical models and Markov chain Monte Carlo (MCMC) techniques forms one of the most profound advances in Bayesian analysis since the 1970s and provides the basis for advances in virtually all areas of applied and theoretical Bayesian statistics.

This volume guides the reader along a statistical journey that begins with the basic structure of Bayesian theory, and then provides details on most of the past and present advances in this field. The book has a unique format. There is an explanatory chapter devoted to each conceptual advance followed by journal-style chapters that provide applications or further advances on the concept.

Thus, the volume is both a textbook and a compendium of papers covering a vast range of topics. It is appropriate for a well-informed novice interested in understanding the basic approach, methods and recent applications. Because of its advanced chapters and recent work, it is also appropriate for a more mature reader interested in recent applications and developments, and who may be looking for ideas that could spawn new research.

Hence, the audience for this unique book would likely include academicians/practitioners, and could likely be required reading for undergraduate and graduate students in statistics, medicine, engineering, scientific computation, business, psychology, bio-informatics, computational physics, graphical models, neural networks, geosciences, and public policy.

The book honours the contributions of Sir Adrian F. M. Smith, one of the seminal Bayesian researchers, with his papers on hierarchical models, sequential Monte Carlo, and Markov chain Monte Carlo and his mentoring of numerous graduate students -- the chapters are authored by prominent statisticians influenced by him.

Bayesian Theory and Applications should serve the dual purpose of a reference book, and a textbook in Bayesian Statistics.

Paul Damien, Professor, McCombs School of Business, University of Texas in Austin,Petros Dellaportas, Professor, Athens University of Economics and Business,Nicholas G. Polson, Professor of Econometrics and Statistics, Chicago Booth, University of Chicago,David A. Stephens, Professor, McGill University

Paul Damien is a Professor at the McCombs School of Business, University of Texas in Austin.


Petros Dellaportas is a Professor at the Athens University of Economics and Business.


Nicholas G Polson is Professor of Econometrics and Statistics at Chicago Booth, University of Chicago.


David M Stephens is a Professor in the Department of Mathematics and Statistics at McGill University, Canada.

Introduction, Paul Damien, Petros Dellaportas, Nicholas G. Polson, David A. Stephens
I EXCHANGEABILITY
1. Observables and Models: exchangeability and the inductive argument, Michael Goldstein
2. Exchangeability and its Ramifications, A. Philip Dawid
II HIERARCHICAL MODELS
3. Hierarchical Modeling, Alan E. Gelfand and Souparno Ghosh
4. Bayesian Hierarchical Kernel Machines for Nonlinear Regression and Classification, Sounak Chakraborty, Bani K Mallick and Malay Ghosh
5. Flexible Bayesian modelling for clustered categorical responses in developmental toxicology, Athanasios Kottas and Kassandra Fronczyk
III MARKOV CHAIN MONTE CARLO
6. Markov chain Monte Carlo Methods, Siddartha Chib
7. Advances in Markov chain Monte Carlo, Jim E. Griffin and David A. Stephens
IV DYNAMIC MODELS
8. Bayesian Dynamic Modelling, Mike West
9. Hierarchical modeling in time series: the factor analytic approach, Dani Gamerman and Esther Salazar
10. Dynamic and spatial modeling of block maxima extremes, Gabriel Huerta and Glenn A. Stark
V SEQUENTIAL MONTE CARLO
11. Online Bayesian learning in dynamic models: An illustrative introduction to particle methods, Hedibert F. Lopes and Carlos M. Carvalho
12. Semi-supervised Classification of Texts Using Particle Learning for Probabilistic Automata, Ana Paula Sales, Christopher Challis, Ryan Prenger, and Daniel Merl
VI NONPARAMETRICS
13. Bayesian Nonparametrics, Stephen G Walker
14. Geometric Weight Priors and their Applications, Ramses H. Mena
15. Revisiting Bayesian Curve Fitting Using Multivariate Normal Mixtures, Stephen G. Walker and George Karabatsos
VII SPLINE MODELS AND COPULAS
16. Applications of Bayesian Smoothing Splines, Sally Wood
17. Bayesian Approaches to Copula Modelling, Michael Stanley Smith
VIII MODEL ELABORATION AND PRIOR DISTRIBUTIONS
18. Hypothesis Testing and Model Uncertainty, M.J. Bayarri and J.O. Berger
19. Proper and non-informative conjugate priors for exponential family models, E. Gutierrez-Pena and M. Mendoza
20. Bayesian Model Specification: Heuristics and Examples, David Draper
21. Case studies in Bayesian screening for time-varying model structure: The partition problem, Zesong Liu, Jesse Windle, and James G. Scott
IX REGRESSIONS AND MODEL AVERAGING
22. Bayesian Regression Structure Discovery, Hugh A. Chipman, Edward I. George and Robert E. McCulloch
23. Gibbs sampling for ordinary, robust and logistic regression with Laplace priors, Robert B. Gramacy
24. Bayesian Model Averaging in the M-Open Framework, Merlise Clyde and Edwin S. Iversen
X FINANCE AND ACTUARIAL SCIENCE
25. Asset Allocation in Finance: A Bayesian Perspective, Eric Jacquier and Nicholas G Polson
26. Markov Chain Monte Carlo Methods in Corporate Finance, Arthur Korteweg
27. Actuarial Credibity Theory and Bayesian Statistics - The Story of a Special Evolution, Udi Makov
XI MEDICINE AND BIOSTATISTICS
28. Bayesian Models in Biostatistics and Medicine, Peter Muller
29. Subgroup Analysis, Purushottam W. Laud, Siva Sivaganesan and Peter Muller
30. Surviving Fully Bayesian Nonparametric Regression Models, Timothy E. Hanson and Alejandro Jara
XII INVERSE PROBLEMS AND APPLICATIONS
31. Inverse Problems, Colin Fox, Heikki Haario and J. Andres Christen
32. Approximate marginalization over modeling errors and uncertainties in inverse problems, Jari Kaipio and Ville Kolehmainen
33. Bayesian reconstruction of particle beam phase space, C. Nakhleh, D. Higdon, C. K. Allen and R. Ryne