Bayesian methods for Variable Selection and Covariance Selection
                  in Multivariate Regression Models.

                        Chris Carter, CSIRO

Abstract:

We consider the Bayesian estimation of regression parameters and an inverse
covariance matrix from Gaussian data.  Methods are given to construct priors
for covariance selection models where the marginal distribution of the model
size has a simple form.  The priors have normalising constants for each
possible model size, rather than for each possible model, which gives a
tractable number of normalising constants that we estimate using Markov
chain Monte Carlo methods and store offline.  Our priors do not require the
restriction that the corresponding graphical models are decomposable.
The effectiveness of variable selection and covariance selection in
estimating the multivariate regression model is assessed using several loss
functions.


** This is joint work with Ed Cripps and Robert Kohn (The University of
New South Wales) and Frederick Wong (The Australian Graduate School
of Management)