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Large incomplete sample robustness in Bayesian networks

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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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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...

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 > 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:

Status:

Not Peer Reviewed

Access rights to Published version:

Open Access

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