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Importance sampling : intrinsic dimension and computational cost
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Agapiou, Sergios, Papaspiliopoulos, Omiros, Sanz-Alonso, Daniel and Stuart, A. M. (2017) Importance sampling : intrinsic dimension and computational cost. Statistical Science, 32 (3). pp. 405-431. doi:10.1214/17-STS611 ISSN 0883-4237.
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Official URL: http://dx.doi.org/10.1214/17-STS611
Abstract
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.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
Library of Congress Subject Headings (LCSH): | Mathematical statistics, Sampling (Statistics) | |||||||||
Journal or Publication Title: | Statistical Science | |||||||||
Publisher: | American Institute of Mathematical Statistics | |||||||||
ISSN: | 0883-4237 | |||||||||
Official Date: | 1 September 2017 | |||||||||
Dates: |
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Volume: | 32 | |||||||||
Number: | 3 | |||||||||
Page Range: | pp. 405-431 | |||||||||
DOI: | 10.1214/17-STS611 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Date of first compliant deposit: | 8 December 2017 | |||||||||
Date of first compliant Open Access: | 8 December 2017 | |||||||||
RIOXX Funder/Project Grant: |
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