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Seminars: Dept Seminar


Computational Approaches for Empirical Bayes Methods and Bayesian Sensitivity Analysis

Date: Monday, March 26
Time: 4:10 am -- 5:00 pm
Place: Snedecor 3105
Speaker: Hani Doss, Department of Statistics, University of Florida, Gainesville, FL

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.