Statistics Colloquium: Dr. Joyee Ghosh
Univ of Iowa
Title: Some Advances in Bayesian Regression Models
Abstract: In this talk, we discuss two recent problems in Bayesian regression, concerning logistic and linear regression models. Gelman et al. (2008) recommended Cauchy priors for the regression coefficients in logistic regression. As the mean does not exist for the Cauchy distribution, a natural question is whether the posterior means of the regression coefficients exist. We provide some conditions for the existence of posterior means and discuss the implications of these results in practice, using simulated and real datasets. This is joint work with Yingbo Li and Robin Mitra. In the second part of the talk, we focus on models/algorithms for Bayesian variable selection in linear regression with
error distributions that are heavier tailed than the normal distribution. We use simulated and real data to demonstrate some of the advantages of
these models compared to their traditional normal error counterparts.