Isoseparation and robustness in finite parameter Bayesian inference
Smith, J. Q., 1953- and Rigat, Fabio, 1975- (2007) Isoseparation and robustness in finite parameter Bayesian inference. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2007 (No.22).
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Under a new family of separations the distance between two posterior densities is the same as the distance between their prior densities
whatever the observed likelihood when that likelihood is strictly positive. Local versions of such separations form the basis of a weak
topology having close links to the Euclidean metric on the natural
parameters of two exponential family densities. Using these local separation measures it is shown that when the tails of the approximating
density have appropriate properties, the variation distance between an
approximating posterior density to a genuine density can be bounded
explicitly. These bounds apply irrespective of whether the prior densities are grossly misspecified with respect to variation distance and
irrespective of the form or the validity of the observed likelihood.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics|
|Library of Congress Subject Headings (LCSH):||Mathematical statistics|
|Series Name:||Working papers|
|Publisher:||University of Warwick. Centre for Research in Statistical Methodology|
|Place of Publication:||Coventry|
|Number of Pages:||23|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
 Andrade, J. A. A. and O’Hagan, A. (2006). “Bayesian robustness mod-
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