Monte Carlo statistical methods, particularly those based on Markov
chains, are now an essential component of the standard set of
techniques used by statisticians. This new edition has been revised
towards a coherent and flowing coverage of these simulation
techniques, with incorporation of the most recent developments in
the field. In particular, the introductory coverage of random
variable generation has been totally revised, with many concepts
being unified through a fundamental theorem of simulation
There are five completely new chapters that cover Monte Carlo
control, reversible jump, slice sampling, sequential Monte Carlo,
and perfect sampling. There is a more in-depth coverage of Gibbs
sampling, which is now contained in three consecutive chapters. The
development of Gibbs sampling starts with slice sampling and its
connection with the fundamental theorem of simulation, and builds
up to two-stage Gibbs sampling and its theoretical properties. A
third chapter covers the multi-stage Gibbs sampler and its variety
of applications. Lastly, chapters from the previous edition have
been revised towards easier access, with the examples getting more
detailed coverage.
This textbook is intended for a second year graduate course, but
will also be useful to someone who either wants to apply simulation
techniques for the resolution of practical problems or wishes to
grasp the fundamental principles behind those methods. The authors
do not assume familiarity with Monte Carlo techniques (such as
random variable generation), with computer programming, or with any
Markov chain theory (the necessary concepts are developed in
Chapter 6). A solutions manual, which coversapproximately 40% of
the problems, is available for instructors who require the book for
a course.
Christian P. Robert is Professor of Statistics in the Applied
Mathematics Department at UniversitA(c) Paris Dauphine, France. He
is also Head of the Statistics Laboratory at the Center for
Research in Economics and Statistics (CREST) of the National
Institute for Statistics and Economic Studies (INSEE) in Paris, and
Adjunct Professor at Ecole Polytechnique. He has written three
other books, including The Bayesian Choice, Second Edition,
Springer 2001. He also edited Discretization and MCMC Convergence
Assessment, Springer 1998. He has served as associate editor for
the Annals of Statistics and the Journal of the American
Statistical Association. He is a fellow of the Institute of
Mathematical Statistics, and a winner of the Young Statistician
Award of the SocietiA(c) de Statistique de Paris in 1995.
George Casella is Distinguished Professor and Chair, Department
of Statistics, University of Florida. He has served as the Theory
and Methods Editor of the Journal of the American Statistical
Association and Executive Editor of Statistical Science. He has
authored three other textbooks: Statistical Inference, Second
Edition, 2001, with Roger L. Berger; Theory of Point Estimation,
1998, with Erich Lehmann; and Variance Components, 1992, with
Shayle R. Searle and Charles E. McCulloch. He is a fellow of the
Institute of Mathematical Statistics and the American Statistical
Association, and an elected fellow of the International Statistical
Institute.
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