Smith, J. Q. and Daneshkhah, Alireza (2008) Large incomplete sample robustness in Bayesian networks. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2008 (No.12).

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Abstract

Under local DeRobertis (LDR) separation measures, the posterior distances between two densities is the same as between the prior densities. Like Kullback -
Leibler separation they also are additive under factorization. These two properties
allow us the prove that the precise specification of the prior will not be critical with
respect to the variation distance on the posteriors under the following conditions.
The genuine and approximating prior need to be similarly rough, the approximating
prior has concentrated on a small ball on the margin of interest, not on the boundary of the probability space, and the approximating prior has similar or fatter tails
to the genuine prior. Robustness then follows for all likelihoods, even ones that
are misspecified. Furthermore, the variation distances can be bounded explicitly by
a easy to calculate function the prior LDR and simple summary statistics of the
functioning posterior. In this paper we apply these results to study the robustness
of prior specification to learning Bayesian Networks.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH):	Robust statistics, Bayesian statistical decision theory
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Official Date:	2008
Dates:	Date Event 2008 Published
Volume:	Vol.2008
Number:	No.12
Number of Pages:	15
Institution:	University of Warwick
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	1 August 2016
Date of first compliant Open Access:	1 August 2016

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