K.C.S.Pillai Memorial Lecture

Objective Prior Distributions in Multivariate Normal Settings

James O. Berger
The Arts and Sciences Professor of Statistics
Institute of Statistics and Decision Sciences, Duke University and Director, Statistical and Applied Mathematical Sciences Institute

Start Date and Time: Fri, 14 May 2004, 4:30 PM

End Date and Time: Fri, 14 May 2004, 5:30 PM

Venue: MATH 175

Refreshments: Refreshments will be served in the Math Library at 4:00 p.m.

Abstract:

In spite of the pervasive use of hierarchical or multilevel linear models in Bayesian analysis, there are not widely accepted objective hyperprior distributions available for their analysis. The difficulty is apparent even with the bivariate normal distribution, for which there exist a host of competing objective priors.

Issues are introduced through a quick look at the bivariate normal distribution (where there are also interesting historical connections to fiducial analysis). Then a prototypical hierarchical model is considered - for which specific posterior propriety, admissibility and computational results are available - and this will be used to make general suggestions as to suitable hyperpriors.