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Qualitative Robustness in Bayesian Inference

Owhadi, Houman and Scovel, Clint (2017) Qualitative Robustness in Bayesian Inference. ESAIM: Probability and Statistics, 21 . pp. 251-274. ISSN 1292-8100. https://resolver.caltech.edu/CaltechAUTHORS:20160223-152453383

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Abstract

The practical implementation of Bayesian inference requires numerical approximation when closed-form expressions are not available. What types of accuracy (convergence) of the numerical approximations guarantee robustness and what types do not? In particular, is the recursive application of Bayes’ rule robust when subsequent data or posteriors are approximated? When the prior is the push forward of a distribution by the map induced by the solution of a PDE, in which norm should that solution be approximated? Motivated by such questions, we investigate the sensitivity of the distribution of posterior distributions (i.e. of posterior distribution-valued random variables, randomized through the data) with respect to perturbations of the prior and data-generating distributions in the limit when the number of data points grows towards infinity.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1051/ps/2017014DOIArticle
https://www.esaim-ps.org/articles/ps/abs/2017/01/ps170014s/ps170014s.htmlPublisherArticle
http://arxiv.org/abs/1411.3984arXivDiscussion Paper
ORCID:
AuthorORCID
Owhadi, Houman0000-0002-5677-1600
Scovel, Clint0000-0001-7757-3411
Alternate Title:Qualitative Robustness of Bayesian Inference
Additional Information:© 2017 EDP Sciences, SMAI. Received: 17 May 2016; Revised: 5 May 2017; Accepted: 21 July 2017. The authors gratefully acknowledge this work supported by the Air Force Office of Scientific Research under Award Number FA9550-12-1-0389 (Scientific Computation of Optimal Statistical Estimators).
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-12-1-0389
Subject Keywords:Bayesian inference; qualitative robustness; stability; Hampel
Classification Code:Mathematics Subject Classification: 62F15; 62F35
Record Number:CaltechAUTHORS:20160223-152453383
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160223-152453383
Official Citation:Qualitative Robustness in Bayesian Inference. Houman Owhadi and Clint Scovel. ESAIM: PS, 21 (2017) 251-274. DOI: https://doi.org/10.1051/ps/2017014
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64689
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:24 Feb 2016 00:14
Last Modified:03 Oct 2019 09:40

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