Population Monte Carlo algorithm in high dimensions

Lee, Jeong Lee, McVinish, Ross and Mengersen, Kerrie (2011) Population Monte Carlo algorithm in high dimensions. Methodology and Computing in Applied Probability, 13 2: 369-389. doi:10.1007/s11009-009-9154-2


Author Lee, Jeong Lee
McVinish, Ross
Mengersen, Kerrie
Title Population Monte Carlo algorithm in high dimensions
Journal name Methodology and Computing in Applied Probability   Check publisher's open access policy
ISSN 1387-5841
1573-7713
Publication date 2011-06
Sub-type Article (original research)
DOI 10.1007/s11009-009-9154-2
Volume 13
Issue 2
Start page 369
End page 389
Total pages 21
Place of publication New York, NY, United States
Publisher Springer New York
Collection year 2012
Language eng
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.
Keyword Asymptotic variance of estimate
Central limit theorem
Importance sampling
Markov chain Monte Carlo
Population Monte Carlo
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2012 Collection
 
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Created: Tue, 20 Sep 2011, 11:52:26 EST by Dr Ross Mcvinish on behalf of Mathematics