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Brittleness of Bayesian inference under finite information in a continuous world
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Owhadi, Houman, Scovel, Clint and Sullivan, Tim J. (2015) Brittleness of Bayesian inference under finite information in a continuous world. Electronic Journal of Statistics, 9 (1). pp. 1-79. doi:10.1214/15-EJS989 ISSN 1935-7524.
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Official URL: http://dx.doi.org/10.1214/15-EJS989
Abstract
We derive, in the classical framework of Bayesian sensitivity analysis, optimal lower and upper bounds on posterior values obtained from Bayesian models that exactly capture an arbitrarily large number of finite-dimensional marginals of the data-generating distribution and/or that are as close as desired to the data-generating distribution in the Prokhorov or total variation metrics; these bounds show that such models may still make the largest possible prediction error after conditioning on an arbitrarily large number of sample data measured at finite precision. These results are obtained through the development of a reduction calculus for optimization problems over measures on spaces of measures. We use this calculus to investigate the mechanisms that generate brittleness/robustness and, in particular, we observe that learning and robustness are antagonistic properties. It is now well understood that the numerical resolution of PDEs requires the satisfaction of specific stability conditions. Is there a missing stability condition for using Bayesian inference in a continuous world under finite information?
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
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| Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Mathematics |
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| Library of Congress Subject Headings (LCSH): | Bayesian statistical decision theory, Brittleness, Finite model theory, Differential equations, Partial, Finite differences | ||||||
| Journal or Publication Title: | Electronic Journal of Statistics | ||||||
| Publisher: | Institute of Mathematical Statistics | ||||||
| ISSN: | 1935-7524 | ||||||
| Official Date: | 2 February 2015 | ||||||
| Dates: |
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| Volume: | 9 | ||||||
| Number: | 1 | ||||||
| Page Range: | pp. 1-79 | ||||||
| DOI: | 10.1214/15-EJS989 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Reuse Statement (publisher, data, author rights): | "The right to place the final version of this article (exactly as published in the journal) on their own homepage or in a public digital repository, provided there is a link to the official journal site." | ||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||
| Date of first compliant deposit: | 15 April 2020 | ||||||
| Date of first compliant Open Access: | 15 April 2020 | ||||||
| RIOXX Funder/Project Grant: |
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