Open Access
August 2017 Importance Sampling: Intrinsic Dimension and Computational Cost
S. Agapiou, O. Papaspiliopoulos, D. Sanz-Alonso, A. M. Stuart
Statist. Sci. 32(3): 405-431 (August 2017). DOI: 10.1214/17-STS611


The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee accurate approximations. Intuitively, some notion of distance between the target and the proposal should determine the computational cost of the method. A major challenge is to quantify this distance in terms of parameters or statistics that are pertinent for the practitioner. The subject has attracted substantial interest from within a variety of communities. The objective of this paper is to overview and unify the resulting literature by creating an overarching framework. A general theory is presented, with a focus on the use of importance sampling in Bayesian inverse problems and filtering.


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S. Agapiou. O. Papaspiliopoulos. D. Sanz-Alonso. A. M. Stuart. "Importance Sampling: Intrinsic Dimension and Computational Cost." Statist. Sci. 32 (3) 405 - 431, August 2017.


Published: August 2017
First available in Project Euclid: 1 September 2017

zbMATH: 06870253
MathSciNet: MR3696003
Digital Object Identifier: 10.1214/17-STS611

Keywords: Absolute continuity , Filtering , importance sampling , Inverse problems , notions of dimension , small noise

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.32 • No. 3 • August 2017
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