This is a graduate-level textbook on Bayesian analysis blending modern Bayesian theory, methods, and applications. Starting from basic statistics, undergraduate calculus and linear algebra, ideas of both subjective and objective Bayesian analysis are developed to a level where real-life data can be analyzed using the current techniques of statistical computing.

Advances in both low-dimensional and high-dimensional problems are covered, as well as important topics such as empirical Bayes and hierarchical Bayes methods and Markov chain Monte Carlo (MCMC) techniques.

Many topics are at the cutting edge of statistical research. Solutions to common inference problems appear throughout the text along with discussion of what prior to choose. There is a discussion of elicitation of a subjective prior as well as the motivation, applicability, and limitations of objective priors. By way of important applications the book presents microarrays, nonparametric regression via wavelets as well as DMA mixtures of normals, and spatial analysis with illustrations using simulated and real data. Theoretical topics at the cutting edge include high-dimensional model selection and Intrinsic Bayes Factors, which the authors have successfully applied to geological mapping.

The style is informal but clear. Asymptotics is used to supplement simulation or understand some aspects of the posterior.

On behalf of those of us who in various ways have con tributed to this volume, and on behalf of all of his colleagues, students and friends throughout the world-wide scientific com munity, we dedicate this volume to Gopinath Kallianpur as a tribute to his work and in appreciation for the insights which he has so graciously and generously offered, and continues to offer, to all of us. Stochastic Processes contains 41 articles related to and frequently influ enced by Kallianpur's work. We regret that space considerations prevented us from including contributions from his numerous colleagues (at North Carolina, lSI, Minnesota, Michigan), former students, co-authors and other eminent scientists whose work is akin to Kallianpur's. This would have taken several more volumes All articles have been refereed, and for their valuable assistance in this we thank many of the contributing authors, as well as: R. Bradley, M.H.A. Davis, R. Davis, J. Hawkins, J. Horowitz, C. Houdre, N.C. Jain, C. Ji, P. Kokoszka, T. Kurtz, K.S. Lau, W. Linde, D. Monrad, D. Stroook, D. Surgailis and S. Yakowitz. We also thank June Maxwell for editorial assistance, Peggy Ravitch for help with the production of the volume, and Lisa Brooks for secretarial assistance. Finally, we are indebted to Dr. Martin Gilchrist, the Statistics editor, and the Springer editorial board for their excellent cooperation and enthusiastic support throughout this project."

This is a graduate-level textbook on Bayesian analysis blending modern Bayesian theory, methods, and applications. Starting from basic statistics, undergraduate calculus and linear algebra, ideas of both subjective and objective Bayesian analysis are developed to a level where real-life data can be analyzed using the current techniques of statistical computing.

Advances in both low-dimensional and high-dimensional problems are covered, as well as important topics such as empirical Bayes and hierarchical Bayes methods and Markov chain Monte Carlo (MCMC) techniques.

Many topics are at the cutting edge of statistical research. Solutions to common inference problems appear throughout the text along with discussion of what prior to choose. There is a discussion of elicitation of a subjective prior as well as the motivation, applicability, and limitations of objective priors. By way of important applications the book presents microarrays, nonparametric regression via wavelets as well as DMA mixtures of normals, and spatial analysis with illustrations using simulated and real data. Theoretical topics at the cutting edge include high-dimensional model selection and Intrinsic Bayes Factors, which the authors have successfully applied to geological mapping.

The style is informal but clear. Asymptotics is used to supplement simulation or understand some aspects of the posterior.