Large deviations for weighted empirical measures arising in importance sampling
2016 (English)In: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 126, no 1Article in journal (Refereed) Published
Importance sampling is a popular method for efficient computation of various properties of a distribution such as probabilities, expectations, quantiles etc. The output of an importance sampling algorithm can be represented as a weighted empirical measure, where the weights are given by the likelihood ratio between the original distribution and the sampling distribution. In this paper the efficiency of an importance sampling algorithm is studied by means of large deviations for the weighted empirical measure. The main result, which is stated as a Laplace principle for the weighted empirical measure arising in importance sampling, can be viewed as a weighted version of Sanov's theorem. The main theorem is applied 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 proof of the main theorem relies on the weak convergence approach to large deviations developed by Dupuis and Ellis.
Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 126, no 1
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:kth:diva-117805DOI: 10.1016/j.spa.2015.08.002ISI: 000366535500006ScopusID: 2-s2.0-84948440031OAI: oai:DiVA.org:kth-117805DiVA: diva2:603116
QC 201601152013-02-052013-02-052016-01-15Bibliographically approved