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Preface
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 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 expan
sive and deep investigation into fundamental Markov chain theory. As the use of MCMC
methods mature, we see deeper theoretical questions addressed, more complex applica
tions 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 12
chapters concerning MCMC foundations, methodology and algorithms. Hie second part
consists of 12 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 oilier 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 dearly 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 applications—there
is just too much of it and its development is moving too fast. Instead, the editorial goal
was to obtain contributions of high quality that may stand the test of time. To this end,
all of the contributions (induding 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 are not indude din this book. Webelieve
the breadth and depth of the contributions to this book, induding some diverse opinions
expressed, imply a continuously bright and dynamic future for MCMC research. We hope
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