webcal

Description

Department Colloquium

Speaker:Professor Bani K. Mallick, Department of Statistics, Texas A&M
University

Title:Bayesian Gaussian Graphical Models and their extensions
Abstract:
Gaussian graphical models (GGMs) are well-established tools for
probabilistic exploration of dependence structures using precision
(inverse covariance) matrices. We propose a Bayesian method for estimating
the precision matrix in GGMs. The method leads

to a sparse and adaptively shrunk estimator of the precision matrix, and
thus conduct model selection and estimation simultaneously. We extend this
method in a regression setup with the presence of covariates. We consider
both the linear as well as the nonlinear

regressions in this GGM framework. Furthermore, to relax the assumption of
the Gaussian distribution, we develop a quantile based approach for sparse
estimation of graphs. We demonstrate that the resulting graph estimator is
robust to outliers and applicable

under general distributional assumptions. We discuss a few applications of
the proposed models.

Professor Bani K. Mallick, Department of Statistics, Texas A&M University