A First Course In Monte Carlo
A COURSE IN MONTE CARLO is a concise explanation of the Monte Carlo (MC) method. In addition to providing guidance for generating samples from diverse distributions, it describes how to design, perform and analyze the results of MC experiments based on independent replications, Markov chain MC, and MC optimization. The text gives considerable emphasis to the variance-reducing techniques of importance sampling, stratified sampling, Rao-Blackwellization, control variates, antithetic variates, and quasi-random numbers. For solving optimization problems it describes several MC techniques, including simulated annealing, simulated tempering, swapping, stochastic tunneling, and genetic algorithms. Examples from many areas show how these techniques perform in practice. Hands-on exercises enable student to experience challenges encountered when solving real problems. An answer key is included.
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Pseudorandom Number Generation
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106 independent replications acceptance-rejection acceptance-rejection method accuracy Algorithm applications software applies approximation Asian options batch bound Chapter computing conditional distribution coordinates cost denote describes efficiency elsewhere equilibrium distribution ergodic estimate evaluation example Exercise H.1 Figure finite Fishman function Gibbs sampling graph Hastings-Metropolis HM sampling Hmin illustration implementation implies importance sampling increases induces initial integer iteration L'Ecuyer lattice LCGs Markov chain MC sampling MCMC MCMC sampling mean number Mersenne twister method Monte Carlo nominating kernel probability problem properties protein provides pseudorandom pseudorandom numbers quasirandom random number random variables randomly sample Rao-Blackwellization recursion reveals rule sample path sample-path length sampling experiment Section selected sequence simulated annealing simulated tempering solution space standard error standard MC statistical step stochastic tunneling stratified sampling subset swap Table techniques temperature Theorem transition kernel uniform distribution values variation warm-up interval Xmin