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Applied Computational Physics$
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Joseph F. Boudreau and Eric. S. Swanson

Print publication date: 2017

Print ISBN-13: 9780198708636

Published to Oxford Scholarship Online: February 2018

DOI: 10.1093/oso/9780198708636.001.0001

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Monte Carlo methods

Monte Carlo methods

Chapter:
(p.196) 7 Monte Carlo methods
Source:
Applied Computational Physics
Author(s):

Joseph F. Boudreau

Eric S. Swanson

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198708636.003.0007

Monte Carlo methods are those designed to obtain numerical answers with the use of random numbers . This chapter discusses random engines, which provide a pseudo-random pattern of bits, and their use in for sampling a variety of nonuniform distributions, for both continuous and discrete variables. A wide selection of uniform and nonuniform variate generators from the C++ standard library are reviewed, and common techniques for generating custom nonuniform variates are discussed. The chapter presents the uses of Monte Carlo to evaluate integrals, particularly multidimensional integrals, and then introduces the important method of Markov chain Monte Carlo, suitable for solving a wide range of scientific problems that require the sampling of complicated multivariate distributions. Relevant topics in probability and statistics are also introduced in this chapter. Finally, the topics of thermalization, autocorrelation, multimodality, and Gibbs sampling are presented.

Keywords:   random variates, probability, statistics, Monte Carlo integration, importance sampling, Markov Chain Monte Carlo, Metropolis-Hastings algorithm, Gibbs sampling

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