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Semi-Exact Control Functionals From Sard's Method

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Semi-Exact Control Functionals From Sard's Method. / South, Leah; Karvonen, Toni; Nemeth, Christopher John; Girolami, Mark; Oates, Chris J.

In: arXiv, 31.01.2020.

Research output: Contribution to journalJournal articlepeer-review

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South L, Karvonen T, Nemeth CJ, Girolami M, Oates CJ. Semi-Exact Control Functionals From Sard's Method. arXiv. 2020 Jan 31.

Author

South, Leah ; Karvonen, Toni ; Nemeth, Christopher John ; Girolami, Mark ; Oates, Chris J. / Semi-Exact Control Functionals From Sard's Method. In: arXiv. 2020.

Bibtex

@article{01e36693cd9e43788e6d33172b697483,
title = "Semi-Exact Control Functionals From Sard's Method",
abstract = "This paper focuses on the numerical computation of posterior expected quantities of interest, where existing approaches based on ergodic averages are gated by the asymptotic variance of the integrand. To address this challenge, a novel variance reduction technique is proposed, based on Sard's approach to numerical integration and the control functional method. The use of Sard's approach ensures that our control functionals are exact on all polynomials up to a fixed degree in the Bernstein-von-Mises limit, so that the reduced variance estimator approximates the behaviour of a polynomially-exact (e.g. Gaussian) cubature method. The proposed estimator has reduced mean square error compared to its competitors, and is illustrated on several Bayesian inference examples. All methods used in this paper are available in the R package ZVCV.",
author = "Leah South and Toni Karvonen and Nemeth, {Christopher John} and Mark Girolami and Oates, {Chris J.}",
year = "2020",
month = jan,
day = "31",
language = "English",
journal = "arXiv",
issn = "2331-8422",

}

RIS

TY - JOUR

T1 - Semi-Exact Control Functionals From Sard's Method

AU - South, Leah

AU - Karvonen, Toni

AU - Nemeth, Christopher John

AU - Girolami, Mark

AU - Oates, Chris J.

PY - 2020/1/31

Y1 - 2020/1/31

N2 - This paper focuses on the numerical computation of posterior expected quantities of interest, where existing approaches based on ergodic averages are gated by the asymptotic variance of the integrand. To address this challenge, a novel variance reduction technique is proposed, based on Sard's approach to numerical integration and the control functional method. The use of Sard's approach ensures that our control functionals are exact on all polynomials up to a fixed degree in the Bernstein-von-Mises limit, so that the reduced variance estimator approximates the behaviour of a polynomially-exact (e.g. Gaussian) cubature method. The proposed estimator has reduced mean square error compared to its competitors, and is illustrated on several Bayesian inference examples. All methods used in this paper are available in the R package ZVCV.

AB - This paper focuses on the numerical computation of posterior expected quantities of interest, where existing approaches based on ergodic averages are gated by the asymptotic variance of the integrand. To address this challenge, a novel variance reduction technique is proposed, based on Sard's approach to numerical integration and the control functional method. The use of Sard's approach ensures that our control functionals are exact on all polynomials up to a fixed degree in the Bernstein-von-Mises limit, so that the reduced variance estimator approximates the behaviour of a polynomially-exact (e.g. Gaussian) cubature method. The proposed estimator has reduced mean square error compared to its competitors, and is illustrated on several Bayesian inference examples. All methods used in this paper are available in the R package ZVCV.

M3 - Journal article

JO - arXiv

JF - arXiv

SN - 2331-8422

ER -