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On the error in Laplace approximations of high-dimensional integrals

On the error in Laplace approximations of high-dimensional integrals
On the error in Laplace approximations of high-dimensional integrals
Laplace approximations are commonly used to approximate high-dimensional integrals in statistical applications, but the quality of such approximations as the dimension of the integral grows is not well understood. In this paper, we provide a new result on the size of the error in first- and higher-order Laplace approximations, in terms of the rate of growth of information about each of the integrated variables. By contrast with many existing results, we allow for variation in the rate of information growth among the different integrated variables. We apply our results to investigate the quality of Laplace approximations to the likelihood in some generalized linear mixed models.
2049-1573
Ogden, Helen
78b03322-3836-4d3b-8b84-faf12895854e
Ogden, Helen
78b03322-3836-4d3b-8b84-faf12895854e

Ogden, Helen (2021) On the error in Laplace approximations of high-dimensional integrals. Stat, 10 (1), [e380]. (doi:10.1002/sta4.380).

Record type: Article

Abstract

Laplace approximations are commonly used to approximate high-dimensional integrals in statistical applications, but the quality of such approximations as the dimension of the integral grows is not well understood. In this paper, we provide a new result on the size of the error in first- and higher-order Laplace approximations, in terms of the rate of growth of information about each of the integrated variables. By contrast with many existing results, we allow for variation in the rate of information growth among the different integrated variables. We apply our results to investigate the quality of Laplace approximations to the likelihood in some generalized linear mixed models.

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On the error in Laplace approximations of high-dimensional integrals - Accepted Manuscript
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More information

Accepted/In Press date: 26 March 2021
e-pub ahead of print date: 6 April 2021
Published date: December 2021
Additional Information: Publisher Copyright: © 2021 The Author. Stat published by John Wiley & Sons Ltd.

Identifiers

Local EPrints ID: 424638
URI: http://eprints.soton.ac.uk/id/eprint/424638
ISSN: 2049-1573
PURE UUID: 17b08ea3-6179-4c5e-a475-d094ec52b7cb
ORCID for Helen Ogden: ORCID iD orcid.org/0000-0001-7204-9776

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Date deposited: 05 Oct 2018 11:39
Last modified: 16 Mar 2024 07:01

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