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Brittleness of Bayesian inference under finite information in a continuous world

Owhadi, Houman and Scovel, Clint and Sullivan, Tim (2015) Brittleness of Bayesian inference under finite information in a continuous world. Electronic Journal of Statistics, 9 (1). pp. 1-79. ISSN 1935-7524. https://resolver.caltech.edu/CaltechAUTHORS:20160108-101302184

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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:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1214/15-EJS989DOIArticle
http://projecteuclid.org/euclid.ejs/1422885673PublisherArticle
http://arxiv.org/abs/1304.6772arXivDiscussion Paper
ORCID:
AuthorORCID
Owhadi, Houman0000-0002-5677-1600
Scovel, Clint0000-0001-7757-3411
Additional Information:© 2015 Institute of Mathematical Statistics. The authors gratefully acknowledge support for this work from the Air Force Office of Scientific Research under Award FA9550-12-1-0389 (Scientific Computation of Optimal Statistical Estimators). We thank P. Diaconis, D. Mayo, P. Stark, and L. Wasserman for stimulating discussions and relevant references and pointers. We thank the anonymous referees for detailed comments and suggestions.
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-12-1-0389
Subject Keywords:Bayesian inference, misspecification, robustness, uncertainty quantification, optimal uncertainty quantification
Issue or Number:1
Classification Code:MSC 2010 subject classifications: Primary 62F15, 62G35; secondary 62A01, 62E20, 62F12, 62G20
Record Number:CaltechAUTHORS:20160108-101302184
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160108-101302184
Official Citation:Owhadi, Houman; Scovel, Clint; Sullivan, Tim. Brittleness of Bayesian inference under finite information in a continuous world. Electron. J. Statist. 9 (2015), no. 1, 1--79. doi:10.1214/15-EJS989. http://projecteuclid.org/euclid.ejs/1422885673.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:63492
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 Jan 2016 20:21
Last Modified:03 Oct 2019 09:28

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