Handbook of Markov Chain Monte Carlo

Edited by Steve Brooks, Andrew Gelman, Galin L. Jones and Xiao-Li Meng

From the Preface by Steve Brooks, Andrew Gelman, Galin L. Jones and Xiao-Li Meng

Over the past 20 years or so Markov chain Monte Carlo (MCMC) methods have revolutionized statistical computing. They have impacted the practice of Bayesian statistics profoundly by allowing intricate models to be posited and \textit{used} in an astonishing array of disciplines as diverse as fisheries science and economics. Of course, Bayesians are not the only ones to benefit from using MCMC and there continues to be increasing use of MCMC in other statistical settings. The practical importance of MCMC has also sparked expansive and deep investigation into fundamental Markov chain theory. As the use of MCMC methods mature we see deeper theoretical questions addressed, more complex applications undertaken and their use spreading to new fields of study. It seemed to us that it was a good time to try to collect an overview of MCMC research and its applications.

This book is intended to be a reference (not a text) for a broad audience and to be of use both to developers and users of MCMC methodology. There is enough introductory material in the book to help graduate students as well as researchers new to MCMC who wish to become acquainted with the basic theory, algorithms and applications. The book should also be of particular interest to those involved in the development or application of new and advanced MCMC methods. Given the diversity of disciplines that use MCMC it seemed prudent to have many of the chapters devoted to detailed examples and case studies of realistic scientific problems. Those wanting to see current practice in MCMC will find a wealth of material to choose from here.

Roughly speaking we can divide the book into two parts. The first part encompasses twelve chapters concerning MCMC foundations, methodology and algorithms. The second part consists of twelve chapters which consider the use of MCMC in practical applications. Within the first part the authors take such a wide variety of approaches that it seems pointless to try to classify the chapters into subgroups. For example, some chapters attempt to appeal to a broad audience by taking a tutorial approach while other chapters, even if introductory, are either more specialized or present more advanced material. Yet others present original research. In the second part the focus shifts to applications. Here again we see a variety of topics but there are two basic approaches taken by the authors of these chapters. The first is to provide an overview of an application area with the goal of identifying best MCMC practice in the area through extended examples. The second approach is to provide detailed case studies of a given problem while clearly identifying the statistical and MCMC-related issues encountered in the application.

When we were planning this book we quickly realized that no single source can give a truly comprehensive overview of cutting-edge MCMC research and application-there is just too much of it and its development is moving too fast. Instead the editorial goal was to obtain contributions high quality that may stand the test of time. To this end all the contributions (including those written by members of the editorial panel) were submitted to a rigorous peer review process and many underwent several revisions. Some contributions, even after revisions, were deemed unacceptable for publication here and we certainly welcome constructive feedback on the chapters that did survive our editorial process. We thank all the authors for their efforts and patience in this process, and we ask for understanding from those whose contributions did not make into this book. We believe the breadth and depth of the contributions to this book, including some diverse opinions expressed, imply a continuously bright and dynamic future for MCMC research. We hope this book inspires further work-- theoretical, methodological, and applied in this exciting and rich area.

Finally, no project of this magnitude could be completed with satisfactory outcome without many individuals' help. We especially want to thank Robert Calver of Chapman & Hall/CRC for his encouragements, guidelines, and particularly his patience during the entire process of editing this book. We also offer our heartfelt thanks to numerous referees for their insightful and rigorous reviews. Of course, the ultimate appreciation for all individuals involved in this project comes from your satisfaction with the book or at least a part of it. So we thank you for reading it.