Hani Doss
Department of Statistics
University of Florida

TITLE:
Computational Approaches for Empirical Bayes Methods and Bayesian
Sensitivity Analysis.

ABSTRACT:
We consider situations in Bayesian analysis where the prior on the
parameter theta is indexed by a hyperparameter h which varies
continuously over a space H, and we deal with two related problems.
The first involves sensitivity analysis and is stated as follows.
Suppose we fix a function f of theta.  How do we efficiently
estimate the posterior expectation of f(theta) simultaneously for
all hyperparameter values?  The second problem is how do we identify
subsets of the hyperparameter space H which give rise to reasonable
choices of h? We assume that we are able to generate Markov chain
samples from the posterior for a finite number of the priors, and we
develop a methodology for dealing with these two problems.  The
methodology applies very generally, and we show how it applies in
particular to a commonly used model for Bayesian variable selection
in linear regression, and give an illustration on a data set
involving a large number of predictor variables.  

This is joint work with Eugenia Buta