School Seminars and Colloquia

Objective Bayesian Analysis for Multivariate Normal Models

Statistics Seminar

by Professor Dongchu Sun


Institution: University of Missouri, USA
Date: Tue 15th July 2008
Time: 1:15 PM
Location: Room 213, Richard Berry Bldg, The University of Melbourne

Abstract: Objective Bayesian inference for the multivariate normal distribution is
illustrated, using different types of formal objective priors (Jeffreys,
invariant, reference and matching), different modes of inference (Bayesian
and frequentist), and different criteria involved in selecting optimal
objective
priors (ease of computation, frequentist performance, marginalization
paradoxes, and decision-theoretic evaluation).


In the course of the investigation of the bivariate normal model, a variety
of surprising results were found, including the availability of objective
priors that yield exact frequentist inferences for many functions of the
bivariate
normal parameters, such as the correlation coefficient. Certain of these
results are generalized to the multivariate normal situation.


The notion of constructive random posteriors is introduced. It is very
powerful for Bayesian computation. Furthermore, it is crucial in proving
the exact
frequentist matching of a large class of objective priors. Various
applications to environmental, ecological, and epidemiological study are
explored.

For More Information: Guoqi Qian g.qian@ms.unimelb.edu.au