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Local robustness of Bayesian parametric inference and observed likelihoods

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Smith, J. Q. (2007) Local robustness of Bayesian parametric inference and observed likelihoods. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2007 (No.9).

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

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

Official Date:

2007

Dates:

Date	Event
2007	Published

Volume:

Vol.2007

Number:

No.9

Number of Pages:

Status:

Not Peer Reviewed

Access rights to Published version:

Open Access

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