Seminars: Dept Seminar
Computational Approaches for Empirical Bayes Methods and Bayesian Sensitivity Analysis
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.