Population Monte Carlo Algorithm in High Dimensions

Jeong Eun Lee (), Ross McVinish () and Kerrie Mengersen ()
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Jeong Eun Lee: Queensland University of Technology
Ross McVinish: The University of Queensland
Kerrie Mengersen: Queensland University of Technology

Methodology and Computing in Applied Probability, 2011, vol. 13, issue 2, 369-389

Abstract: Abstract 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.

Keywords: Asymptotic variance of estimate; Central limit theorem; Importance sampling; Markov chain Monte Carlo; Population Monte Carlo; 65C05; 65C60 (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s11009-009-9154-2

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