Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Nov, 1991, Volume 59, Issue 6

Robust HPD Regions in Bayesian Regression Models<1581:RHRIBR>2.0.CO;2-A
p. 1581-1589

Klaus Potzelberger, Wolfgang Polasek

A Bayesian analysis of the linear regression model with only parts of the prior distribution specified or a robust Bayesian analysis lead to sets of posterior distributions. The so-called feasible ellipsoid of Leamer (1978) describes the region of posterior means if for conjugate priors the prior covariance matrix is varying in the set of symmetric positive-definite matrices. As an extension to Bayesian confidence sets (HPD regions, i.e. regions of highest posterior probability) we introduce the concept of HiFi (high fiduciary) regions. The HiFi region is a union of HPD regions, and is a tool for describing the dependence of the posterior distribution on the prior covariance. In this paper we assume that the prior covariance matrix varies in an interval of positive definite matrices.

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