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Monte Carlo Methods, Volume 1

Basics

Monte Carlo Methods, Volume 1 by Malvin H. Kalos
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This introduction to Monte Carlo Methods seeks to identify andstudy the unifying elements that underlie their effectiveapplication. It focuses on two basic themes. The first is theimportance of random walks as they occur both in natural stochasticsystems and in their relationship to integral and differentialequations. The second theme is that of variance reduction ingeneral and importance sampling in particular as a technique forefficient use of the methods. Random walks are introduced with anelementary example in which the modelling of radiation transportarises directly from a schematic probabilistic description of theinteraction of radiation with matter. Building on that example, therelationship between random walks and integral equations isoutlined. The applicability of these ideas to other problems isshown by a clear and elementary introduction to the solution of theSchrodinger equation by random walks.
The detailed discussion of variance reduction includes Monte Carloevaluation of finite-dimensional integrals. Special attention isgiven to importance sampling, partly because of its intrinsicinterest in quadrature, partly because of its general usefulness inthe solution of integral equations. One significant feature is thatMonte Carlo Methods treats the "Metropolis algorithm" in thecontext of sampling methods, clearly distinguishing it fromimportance sampling.

Physicists, chemists, statisticians, mathematicians, and computerscientists will find Monte Carlo Methods a complete and stimulatingintroduction.
Wiley; September 2008
198 pages; ISBN 9783527617401
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Title: Monte Carlo Methods, Volume 1
Author: Malvin H. Kalos; Paula A. Whitlock
 
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