Large deviations for weighted empirical measures arising in importance sampling

In this paper the efficiency of an importance sampling algorithm is studied by means of large deviations for the associated weighted empirical measure. The main result, stated as a Laplace principle for these weighted empirical measures, can be viewed as an extension of Sanov’s theorem. The main the...

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Bibliographic Details
Published inStochastic processes and their applications Vol. 126; no. 1; pp. 138 - 170
Main Authors Hult, Henrik, Nyquist, Pierre
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.01.2016
Subjects
Empirical measures
Importance sampling
Large deviations
Monte Carlo
secondary
Large deviations
Monte Carlo
Empirical measures
primary
Importance sampling
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Summary:In this paper the efficiency of an importance sampling algorithm is studied by means of large deviations for the associated weighted empirical measure. The main result, stated as a Laplace principle for these weighted empirical measures, can be viewed as an extension of Sanov’s theorem. The main theorem is used to quantify the performance of an importance sampling algorithm over a collection of subsets of a given target set as well as quantile estimates. The analysis yields an estimate of the sample size needed to reach a desired precision and of the reduction in cost compared to standard Monte Carlo.
ISSN:0304-4149
1879-209X
1879-209X
DOI:10.1016/j.spa.2015.08.002