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On the Brittleness of Bayesian Inference

Owhadi, Houman and Scovel, Clint and Sullivan, Tim (2015) On the Brittleness of Bayesian Inference. SIAM Review, 57 (4). pp. 566-582. ISSN 0036-1445. https://resolver.caltech.edu/CaltechAUTHORS:20160108-105121903

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Abstract

With the advent of high-performance computing, Bayesian methods are becoming increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods can impact the making of sometimes critical decisions in increasingly complicated contexts, the sensitivity of their posterior conclusions with respect to the underlying models and prior beliefs is a pressing question to which there currently exist positive and negative answers. We report new results suggesting that, although Bayesian methods are robust when the number of possible outcomes is finite or when only a finite number of marginals of the data-generating distribution are unknown, they could be generically brittle when applied to continuous systems (and their discretizations) with finite information on the data-generating distribution. If closeness is defined in terms of the total variation (TV) metric or the matching of a finite system of generalized moments, then (1) two practitioners who use arbitrarily close models and observe the same (possibly arbitrarily large amount of) data may reach opposite conclusions; and (2) any given prior and model can be slightly perturbed to achieve any desired posterior conclusion. The mechanism causing brittleness/robustness suggests that learning and robustness are antagonistic requirements, which raises the possibility of a missing stability condition when using Bayesian inference in a continuous world under finite information.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1137/130938633DOIArticle
http://epubs.siam.org/doi/10.1137/130938633PublisherArticle
http://arxiv.org/abs/1308.6306arXivDiscussion Paper
ORCID:
AuthorORCID
Owhadi, Houman0000-0002-5677-1600
Scovel, Clint0000-0001-7757-3411
Additional Information:© 2015 Society for Industrial and Applied Mathematics. Received by the editors September 26, 2013; accepted for publication (in revised form) April 9, 2015; published electronically November 5, 2015. 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). They thank P. Diaconis, D. Mayo, P. Stark, and L. Wasserman for stimulating discussions and relevant references and pointers. They thank the anonymous referees for valuable 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, Bayesian sensitivity analysis
Issue or Number:4
Classification Code:AMS subject classifications. 62F15, 62G35
Record Number:CaltechAUTHORS:20160108-105121903
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160108-105121903
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:63498
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 Jan 2016 20:12
Last Modified:03 Oct 2019 09:29

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