Simple Monte Carlo and the Metropolis algorithm

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Simple Monte Carlo and the Metropolis algorithm
We study the integration of functions with respect to an unknown density. Information is available as oracle calls to the integrand and to the nonnormalized 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.
Peter Mathé, Erich Novak
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2007
Where JC
Authors Peter Mathé, Erich Novak
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