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Strong maximum a posteriori estimation in Banach spaces with Gaussian priors
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Lambley, Hefin (2023) Strong maximum a posteriori estimation in Banach spaces with Gaussian priors. Inverse Problems, 39 (12). 125010. doi:10.1088/1361-6420/ad07a4 ISSN 0266-5611.
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Official URL: http://doi.org/10.1088/1361-6420/ad07a4
Abstract
This article shows that a large class of posterior measures that are absolutely continuous with respect to a Gaussian prior have strong maximum a posteriori estimators in the sense of Dashti et al. (Inverse Probl. 29:095017, 2013). This result holds in any separable Banach space and applies in particular to nonparametric Bayesian inverse problems with additive noise. When applied to Bayesian inverse problems, this significantly extends existing results on maximum a posteriori estimators by relaxing the conditions on the log-likelihood and on the space in which the inverse problem is set.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
Library of Congress Subject Headings (LCSH): | Inverse problems (Differential equations), Bayesian statistical decision theory, Probability measures | |||||||||
Journal or Publication Title: | Inverse Problems | |||||||||
Publisher: | Institute of Physics Publishing Ltd. | |||||||||
ISSN: | 0266-5611 | |||||||||
Official Date: | 7 November 2023 | |||||||||
Dates: |
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Volume: | 39 | |||||||||
Number: | 12 | |||||||||
Article Number: | 125010 | |||||||||
DOI: | 10.1088/1361-6420/ad07a4 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||
Copyright Holders: | © 2023 The Author(s). Published by IOP Publishing Ltd | |||||||||
Date of first compliant deposit: | 30 October 2023 | |||||||||
Date of first compliant Open Access: | 30 October 2023 | |||||||||
RIOXX Funder/Project Grant: |
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