Simple Monte Carlo and the Metropolis Algorithm

Details Simple Monte Carlo and the Metropolis Algorithm Simple Monte Carlo and the Metropolis Algorithm

2006-11-09

arxiv.org/abs/math/0611285v2

Mathematics

Numerical Analysis

Journal of Complexity, to appear

Scientific paper

We study the integration of functions with respect to an unknown density. We compare the simple Monte Carlo method (which is almost optimal for a certain large class of inputs) and compare it with the Metropolis algorithm (based on a suitable ball walk). Using MCMC we prove (for certain classes of inputs) that adaptive methods are much better than nonadaptive ones. Actually, the curse of dimension (for nonadaptive methods) can be broken by adaption.

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