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.
Ogden, Helen
78b03322-3836-4d3b-8b84-faf12895854e
December 2021
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).
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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arxiv
- Author's Original
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On the error in Laplace approximations of high-dimensional integrals
- Accepted Manuscript
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Accepted/In Press date: 26 March 2021
e-pub ahead of print date: 6 April 2021
Published date: December 2021
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Publisher Copyright:
© 2021 The Author. Stat published by John Wiley & Sons Ltd.
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Local EPrints ID: 424638
URI: http://eprints.soton.ac.uk/id/eprint/424638
ISSN: 2049-1573
PURE UUID: 17b08ea3-6179-4c5e-a475-d094ec52b7cb
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Date deposited: 05 Oct 2018 11:39
Last modified: 16 Mar 2024 07:01
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