Monte Carlo Strategies in Scientific Computing

A large number of scientists and engineers use Monte Carlo simulation as an essential tool in their work. This paperback edition (a reprint of the 2001 Springer edition) provides an up-to-date and self-contained summary of recent research results. 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 a textbook for a graduate-level course on Monte Carlo methods. Many problems discussed in the later chapters can be potential thesis topics for masters' or Ph.D. students in statistics or computer science departments.

The author is a leading researcher in a very active area of research Emphasis is on making these methods accessible to scientists who want to apply them Includes examples from artificial intelligence, computational biology, computer vision and chemistry Includes supplementary material: sn.pub/extras

Klappentext

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 masters' 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 MonteCarlo methods, and in the process uncovers and discusses commonalities among seemingly disparate techniques that arose in various areas of application. ... The book is well organized; the flow of topics follows a logical development. ... The coverage is up-to-date and comprehensive, and so the book is a good resource for people conducting research on Monte Carlo methods. ... The book would be an excellent supplementary text for a course in scientific computing ... ." (SIAM Review)

"The strength of this book is in bringing together advanced Monte Carlo (MC) methods developed in many disciplines. ... Throughout the book are examples of techniques invented, or reinvented, in different fields that may be applied elsewhere. ... 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)

Zusammenfassung

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 a textbook for a graduate-level course on Monte Carlo methods.

Inhalt
1 Introduction and Examples.- 2 Basic Principles: Rejection, Weighting, and Others.- 3 Theory of Sequential Monte Carlo.- 4 Sequential Monte Carlo in Action.- 5 Metropolis Algorithm and Beyond.- 6 The Gibbs Sampler.- 7 Cluster Algorithms for the Ising Model.- 8 General Conditional Sampling.- 9 Molecular Dynamics and Hybrid Monte Carlo.- 10 Multilevel Sampling and Optimization Methods.- 11 Population-Based Monte Carlo Methods.- 12 Markov Chains and Their Convergence.- 13 Selected Theoretical Topics.- A Basics in Probability and Statistics.- A.1 Basic Probability Theory.- A.1.1 Experiments, events, and probability.- A.1.2 Univariate random variables and their properties.- A.1.3 Multivariate random variable.- A.1.4 Convergence of random variables.- A.2 Statistical Modeling and Inference.- A.2.1 Parametric statistical modeling.- A.2.2 Frequentist approach to statistical inference.- A.2.3 Bayesian methodology.- A.3 Bayes Procedure and Missing Data Formalism.- A.3.1 The joint and posterior distributions.- A.3.2 The missing data problem.- A.4 The Expectation-Maximization Algorithm.- References.- Author Index.