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Control functionals for Monte Carlo integration

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Title: Control functionals for Monte Carlo integration
Authors: Oates, CJ
Girolami, M
Chopin, N
Item Type: Journal Article
Abstract: A non‐parametric extension of control variates is presented. These leverage gradient information on the sampling density to achieve substantial variance reduction. It is not required that the sampling density be normalized. The novel contribution of this work is based on two important insights: a trade‐off between random sampling and deterministic approximation and a new gradient‐based function space derived from Stein's identity. Unlike classical control variates, our estimators improve rates of convergence, often requiring orders of magnitude fewer simulations to achieve a fixed level of precision. Theoretical and empirical results are presented, the latter focusing on integration problems arising in hierarchical models and models based on non‐linear ordinary differential equations.
Issue Date: 1-Jun-2017
Date of Acceptance: 29-Feb-2016
URI: http://hdl.handle.net/10044/1/66156
DOI: https://dx.doi.org/10.1111/rssb.12185
ISSN: 1369-7412
Publisher: Wiley
Start Page: 695
End Page: 718
Journal / Book Title: Journal of the Royal Statistical Society Series B: Statistical Methodology
Volume: 79
Issue: 3
Copyright Statement: © 2016 Royal Statistical Society. This is the accepted version of the following article: Oates, C. J., Girolami, M. and Chopin, N. (2017), Control functionals for Monte Carlo integration. J. R. Stat. Soc. B, 79: 695-718., which has been published in final form at https://dx.doi.org/10.1111/rssb.12185
Keywords: Science & Technology
Physical Sciences
Statistics & Probability
Control variates
Reproducing kernel
Stein's identity
Variance reduction
0104 Statistics
1403 Econometrics
Publication Status: Published
Online Publication Date: 2016-05-23
Appears in Collections:Mathematics
Faculty of Natural Sciences