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Type: Report × Subject: Monte Carlo methods ×

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Now showing 1 - 2 of 2
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    Simple Monte Carlo and the metropolis algorithm
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Mathé, Peter; Novak, Erich
    We study the integration of functions with respect to an unknown density. Information is available as oracle calls to the integrand and to the non-normalized density function. We are interested in analyzing the integration error of optimal algorithms (or the complexity of the problem) with emphasis on the variability of the weight function. For a corresponding large class of problem instances we show that the complexity grows linearly in the variability, and the simple Monte Carlo method provides an almost optimal algorithm. Under additional geometric restrictions (mainly log-concavity) for the density functions, we establish that a suitable adaptive local Metropolis algorithm is almost optimal and outperforms any non-adaptive algorithm.
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    On non-asymptotic optimal stopping criteria in Monte Carlo simulations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Bayer, Christian; Hoel, Hakon; von Schwerin, Erik; Tempone, Raúl
    We consider the setting of estimating the mean of a random variable by a sequential stopping rule Monte Carlo (MC) method. The performance of a typical second moment based sequential stopping rule MC method is shown to be unreliable in such settings both by numerical examples and through analysis. By analysis and approximations, we construct a higher moment based stopping rule which is shown in numerical examples to perform more reliably and only slightly less efficiently than the second moment based stopping rule.