A class of optimum importance sampling strategies
type: Item
instance of: scholarly article
title: A class of optimum importance sampling strategies
zbMATH Open document ID: 0869.62087
DOI: 10.1016/0020-0255(94)00116-S
author: Geoffrey C. Orsak
author: Behnaam Aazhang
published in: Information Sciences
publication date: 1997-08-04T00:00:00Z
review text: The authors determine the optimal biasing density from a constraint class whose controlling parameter is fundamental in the performance analysis of Importance Sampling. In addition, it is shown that the constrained optimal distribution from this class minimizes every statistical distance measure to the global optimal distribution and as a consequence is optimal with respect to a large family of nonlinear cost functions. Salient features of this distribution are: (1) unlike the unconstrained optimal solution, this distribution can be made independent of the parameter to be estimated and thus can admit to implementation, and (2) this distribution renders performance gains which can be made arbitrarily close to the optimal gains. Applications to estimating probabilities of rare events (e.g., error rates in communication systems) will be presented. Further analysis will show that in this case the savings over Monte Carlo simulations become unbounded as the probability of the rare event diminishes.
Mathematics Subject Classification ID: 62P99
Mathematics Subject Classification ID: 65C05
zbMATH DE Number: 1025624
zbMATH Keywords: importance sampling
zbMATH Keywords: optimal biasing density
zbMATH Keywords: constrained optimal distribution
zbMATH Keywords: statistical distance measure
zbMATH Keywords: global optimal distribution
zbMATH Keywords: nonlinear cost functions
zbMATH Keywords: estimating probabilities of rare events
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1025624