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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.
Table of Contents
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