The Library
Well-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priors
Tools
Tools
Tools
Sullivan, T. J. (2017) Well-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priors. Inverse Problems & Imaging, 11 (5). pp. 857-874. doi:10.3934/ipi.2017040 ISSN 1930-8345.
|
PDF
WRAP-Well-posed-Baysian-heavy-tailed-space-priors-Sullivan-2015.pdf - Accepted Version - Requires a PDF viewer. Download (852Kb) | Preview |
Official URL: http://dx.doi.org/10.3934/ipi.2017040
Abstract
This article extends the framework of Bayesian inverse problems in infinite-dimensional parameter spaces, as advocated by Stuart (Acta Numer. 19:451–559,2010) and others, to the case of a heavy-tailed prior measure in the family of stable distributions, such as an infinite-dimensional Cauchy distribution, for which polynomial moments are infinite or undefined. It is shown that analogues of the Karhunen–Loéve expansion for square-integrable random variables can be used to sample such measures on quasi-Banach spaces. Furthermore, under weaker regularity assumptions than those used to date, the Bayesian posterior measure is shown to depend Lipschitz continuously in the Hellinger metric upon perturbations of the misfit function and observed data.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Mathematics |
||||||
| Library of Congress Subject Headings (LCSH): | Bayesian statistical decision theory, Polynomials, Quasi-uniform spaces, Group Theory, Quasisymmetric groups | ||||||
| Journal or Publication Title: | Inverse Problems & Imaging | ||||||
| Publisher: | American Institute of Mathematical Sciences | ||||||
| ISSN: | 1930-8345 | ||||||
| Official Date: | July 2017 | ||||||
| Dates: |
|
||||||
| Volume: | 11 | ||||||
| Number: | 5 | ||||||
| Page Range: | pp. 857-874 | ||||||
| DOI: | 10.3934/ipi.2017040 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Reuse Statement (publisher, data, author rights): | The following article appeared in Sullivan, T. J. (2017) Well-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priors. Inverse Problems & Imaging, 11 (5). pp. 857-874. and may be found at http://dx.doi.org/10.3934/ipi.2017040 | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Copyright Holders: | Copyright © 2020 American Institute of Mathematical Sciences | ||||||
| Date of first compliant deposit: | 15 April 2020 | ||||||
| Date of first compliant Open Access: | 15 April 2020 | ||||||
| RIOXX Funder/Project Grant: |
|
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
