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An early experiment that conceives the basic idea of Monte Carlo compu tation is known as "Buffon's needle" (Dorrie 1965), first stated by Georges Louis Leclerc Comte de Buffon in 1777. In this well-known experiment, one throws a needle of length l onto a flat surface with a grid of parallel lines with spacing D (D > l). It is easy to compute that, under ideal conditions, the chance that the needle will intersect one of the lines is 2l / 1r D. Thus, if we let PN be the proportion of "intersects" in N throws, we can have an estimate of 1r as 1" 2l 1r= 1m -D, N-too PN which will "converge" to 1r as N increases to infinity. Numerous investiga tors actually used this setting to estimate 1r. The idea of simulating random processes so as to help evaluate certain quantities of interest is now an es sential part of scientific computing. A systematic use of the Monte Carlo method for real scientific prob lems appeared in the early days of electronic computing (1945-55) and accompanied the development of the world's first programmable "super" computer, MANIAC (Mathematical Analyzer, Numerical Integrator and Computer), at Los Alamos during World War II. In order to make a good use of these fast computing machines, scientists (Stanislaw Ulam, John von Neumann, Nicholas Metropolis, Enrico Fermi, etc."

Product Identifiers

PublisherSpringer

ISBN-100387763694

ISBN-139780387763699

eBay Product ID (ePID)109297959

Product Key Features

Publication Year2008

Number of Pages344 Pages

LanguageEnglish

TypeTextbook

AuthorJun S. Liu

SeriesSpringer Series in Statistics

FormatPaperback

Dimensions

Weight39.9 Oz

Length9in

Height0.3in

Width6in

Additional Product Features

GroupScholarly & Professional

Number of Volumes1 Vol.

Dewey Decimal501/.519282

Lc Classification NumberQa276-280qa71-90qa27

ReviewsFrom the reviews: MATHEMATICAL REVIEWS "This book is an excellent survey of current Monte Carlo methods. A strength of the book is the inclusion of a number of applications to current scientific problems. The applications amply demonstrate the relevance of this approach to modern computing. There is a fairly thorough coverage of wide variety of Monte Carlo algorithms that have arisen in diverse fields such as physics, chemistry, biology, etc., and the relationship among them. The book is highly recommended." SHORT BOOK REVIEWS "This is a worthwhile reference to recent advances in sequential Monte Carlo, primarily Bayesian and Markov Chain methods. To those with an interest in these topics, it is worth a read." "This well written book discusses why Monte Carlo techniques are needed, the importance of Monte Carlo in bioinformatics, target tracking in nonlinear dynamic systems, in missing data analysis âŠ . The references are exhaustive. I enjoyed reading this book and learned a lot about the genetic applications of Monte Carlo techniques. I recommend this book highly to statisticians and geneticists." (Ramalingam Shanmugam, Journal of Statistical Computation and Simulation, Vol. 74 (8), 2004) "Markov chain Monte Carlo âŠ was introduced to tackle more sophisticated and realistic statistical models as in the Bayesian approach of statistics. The author is well known in the area of MCMC methods âŠ . The book is written in a proper style âŠ . It provides an actual view of theoretical developments complemented by applications âŠ . It may be highly recommended for scientists and graduate students who want to gain some insight in either the theory or application of advanced Monte Carlo methods." (Ernst Stadlober, Metrika, February, 2004) "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. âŠ The book is well organized; the flow of topics follows a logical development. âŠ The coverage is up-to-date and comprehensive, and so the book is a good resource for people conducting research on Monte Carlo methods. âŠ The book would be an excellent supplementary text for a course in scientific computing âŠ ." (James E. Gentle, SIAM Review, Vol. 44 (3), 2002) "The strength of this book is in bringing together advanced Monte Carlo (MC) methods developed in many disciplines. âŠ Throughout the book are examples of techniques invented, or reinvented, in different fields that may be applied elsewhere. âŠ Monte Carlo Strategies in Scientific Computing offers a large âŠ variety of methods and examples. Those interested in using MC to solve difficult problems will find many ideas, collected from a variety of disciplines, and references for further study." (Tim Hesterberg, Technometrics, Vol. 44 (4), 2002) "This recent addition to the Monte Carlo literature is divided into 13 chapters and an appendix. It provides both the methodology and the underlying theory for applying Monte Carlo techniques to a broad range of problems. âŠ In the Appendix the author outlines the basics in probability theory and statistical inference procedures. âŠ this book is a valuable and recommended reference to Monte Carlo methods; particularly it draws the attention to recent work in sequential Monte Carlo." (Radu Theodorescu, Zentralblatt MATH, Vol. 991, 2002) "The book gives a good introduction to current Monte Carlo methods and explains the terminology on a moderate level of abstraction. It becomes clear that any specific problem needs a tailored algorithm to be efficient. This is the reason for the emergence of variance reduction methods, importance sampling, rejection, sequential MC, Metropolis algorithms, Gibbs samplers, Markov Chain MC (MCMC), or hybrid MC with molecular dynamics. âŠ it is one of the first attempts to show the general principles behind an apparent z

Dewey Edition21

Publication Date2008-01-04

IllustratedYes