Smith, J. Q., 1953- (2007) Local robustness of Bayesian parametric inference and observed likelihoods. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.

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Abstract

Here a new class of local separation measures over prior densities is studied and their usefulness for examining prior to posterior robustness under a sequence of observed likelihoods, possibly erroneous, illustrated. It is shown that provided an approximation to a prior distribution satisfies certain mild smoothness and tail conditions then prior to posterior inference for large samples is robust, irrespective of whether the priors are grossly misspecified with respect to variation distance and irrespective of the form or the validity of the observed likelihood. Furthermore it is usually possible to specify error bounds explicitly in terms of statistics associated with the posterior associated with the approximating prior and asumed prior error bounds. These results apply in a general multivariate setting and are especially easy to interpret when prior densities are approximated using standard families or multivariate prior densities factorise.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Distribution (Probability theory), Bayesian statistical decision theory
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2007
Volume:	Vol.2007
Number:	No.9
Number of Pages:	39
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/35541

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