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Large deviations for weighted empirical measures arising in importance sampling

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  • Hult, Henrik
  • Nyquist, Pierre

Abstract

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.

Suggested Citation

  • Hult, Henrik & Nyquist, Pierre, 2016. "Large deviations for weighted empirical measures arising in importance sampling," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 138-170.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:1:p:138-170
    DOI: 10.1016/j.spa.2015.08.002
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    References listed on IDEAS

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    1. Dean, Thomas & Dupuis, Paul, 2009. "Splitting for rare event simulation: A large deviation approach to design and analysis," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 562-587, February.
    2. Paul Dupuis & Hui Wang, 2007. "Subsolutions of an Isaacs Equation and Efficient Schemes for Importance Sampling," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 723-757, August.
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