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Population Monte Carlo Algorithm in High Dimensions

Author

Listed:
  • Jeong Eun Lee

    (Queensland University of Technology)

  • Ross McVinish

    (The University of Queensland)

  • Kerrie Mengersen

    (Queensland University of Technology)

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.

Suggested Citation

  • Jeong Eun Lee & Ross McVinish & Kerrie Mengersen, 2011. "Population Monte Carlo Algorithm in High Dimensions," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 369-389, June.
  • Handle: RePEc:spr:metcap:v:13:y:2011:i:2:d:10.1007_s11009-009-9154-2
    DOI: 10.1007/s11009-009-9154-2
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/6072 is not listed on IDEAS
    2. Peter Neal & Gareth Roberts, 2008. "Optimal Scaling for Random Walk Metropolis on Spherically Constrained Target Densities," Methodology and Computing in Applied Probability, Springer, vol. 10(2), pages 277-297, June.
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