Population Monte Carlo Algorithm in High Dimensions
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The population Monte Carlo algorithm is an iterative importance sampling scheme for solving static problems. We examine the population Monte Carlo algorithm in a simplified setting, a single step of the general algorithm, and study a fundamental problem that occurs in applying importance sampling to high-dimensional problem. The precision of the computed estimate from the simplified setting is measured by the asymptotic variance of estimate under conditions on the importance function. We demonstrate the exponential growth of the asymptotic variance with the dimension and show that the optimal covariance matrix for the importance function can be estimated in special cases.
KeywordsAsymptotic variance of estimate Central limit theorem Importance sampling Markov chain Monte Carlo Population Monte Carlo
AMS 2000 Subject Classifications65C05 65C60
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