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Control functionals for Monte Carlo integration
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Oates, Chris J., Girolami, Mark and Chopin, Nicolas (2017) Control functionals for Monte Carlo integration. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 79 (3). pp. 695-718. doi:10.1111/rssb.12185 ISSN 1369-7412.
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Official URL: http://dx.doi.org/10.1111/rssb.12185
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.
Item Type: | Journal Article | ||||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||
Journal or Publication Title: | Journal of the Royal Statistical Society: Series B (Statistical Methodology) | ||||||||||
Publisher: | Wiley-Blackwell Publishing Ltd. | ||||||||||
ISSN: | 1369-7412 | ||||||||||
Official Date: | June 2017 | ||||||||||
Dates: |
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Volume: | 79 | ||||||||||
Number: | 3 | ||||||||||
Page Range: | pp. 695-718 | ||||||||||
DOI: | 10.1111/rssb.12185 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||
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