A large number of scientists and engineers employ Monte Carlo simulation and related global optimization techniques (such as simulated annealing) as an essential tool in their work. For such scientists, there is a need to keep up to date with several recent advances in Monte Carlo methodologies such as cluster methods, data- augmentation, simulated tempering and other auxiliary variable methods. There is also a trend in moving towards a population-based approach. All these advances in one way or another were motivated by the need to sample from very complex distribution for which traditional methods would tend to be trapped in local energy minima. It is our aim to provide a self-contained and up to date treatment of the Monte Carlo method to this audience. The Monte Carlo method is a computer-based statistical sampling approach for solving numerical problems concerned with a complex system. The methodology was initially developed in the field of statistical physics during the early days of electronic computing (1945-55) and has now been adopted by researchers in almost all scientific fields. The fundamental idea for constructing Markov chain based Monte Carlo algorithms was introduced in the 1950s. This idea was later extended to handle more and more complex physical systems. In the 1980s, statisticians and computer scientists developed Monter Carlo-based algorithms for a wide variety of integration and optimization tasks. In the 1990s, the method began to play an important role in computational biology. Over the past fifty years, reasearchers in diverse scientific fields have studied the Monte Carlo method and contributed to its development. Today, a large number of scientisits andengineers employ Monte Carlo techniques as an essential tool in their work. For such scientists, there is a need to keep up-to-date with recent advances in Monte Carlo methodologies.
This paperback edition is a reprint of the 2001 Springer edition.
This book provides a self-contained and up-to-date treatment of the Monte Carlo method and develops a common framework under which various Monte Carlo techniques can be "standardized" and compared. Given the interdisciplinary nature of the topics and a moderate prerequisite for the reader, this book should be of interest to a broad audience of quantitative researchers such as computational biologists, computer scientists, econometricians, engineers, probabilists, and statisticians. It can also be used as the textbook for a graduate-level course on Monte Carlo methods. Many problems discussed in the alter chapters can be potential thesis topics for mastersa (TM) or Ph.D. students in statistics or computer science departments.
Jun Liu is Professor of Statistics at Harvard University, with a courtesy Professor appointment at Harvard Biostatistics Department. Professor Liu was the recipient of the 2002 COPSS Presidents' Award, the most prestigious one for statisticians and given annually by five leading statistical associations to one individual under age 40. He was selected as a Terman Fellow by Stanford University in 1995, as a Medallion Lecturer by the Institute of Mathematical Statistics (IMS) in 2002, and as a Bernoulli Lecturer by the International Bernoulli Society in 2004. He was elected to the IMS Fellow in 2004 and Fellow of the American Statistical Association in 2005. He and co-workers have published more than 130 research articles and book chapters on Bayesian modeling and computation, bioinformatics, genetics, signal processing, stochastic dynamic systems, Monte Carlo methods, and theoretical statistics.
"An excellent survey of current Monte Carlo methods. The applications amply demonstrate the relevance of this approach to modern computing. The book is highly recommended." (Mathematical Reviews)
"This book provides comprehensive coverage of Monte Carlo methods, and in the process uncovers and discusses commonalities among seemingly disparate techniques that arose in various areas of application. a ] The book is well organized; the flow of topics follows a logical development. a ] The coverage is up-to-date and comprehensive, and so the book is a good resource for people conducting research on Monte Carlo methods. a ] The book would be an excellent supplementary text for a course in scientific computing a ] ." (SIAM Review)
"The strength of this book is in bringing together advanced Monte Carlo (MC) methods developed in many disciplines. a ] Throughout the book are examples of techniques invented, or reinvented, in different fields that may be applied elsewhere. a ] Those interested in using MC to solve difficult problems will find many ideas, collected from a variety of disciplines, and references for further study." (Technometrics)
