Professor Jingqin Rosy Luo
 

Division of Biostatistics, Washington University, School of Medicine
 

Title: Covariance selection and Bayes classification via shrinkage
 

Abstract: Due to the positive definiteness constraint and the rapidly-growing number of parameters with dimensions, covariance estimation in a multivariate normal population has been a classic but challenging statistical problem. Many approaches shrink a covariance/precision matrix toward some special parsimonious structures, which may suffer from misspecification error. By describing the covariance selection problem as a system of linear recursive equations, we work in the Cholesky decomposition framework of a precision matrix. Through application of Bayesian shrinkage regressions, we obtain robust estimators for a precision matrix of a flexible sparse pattern. A further application of Bayesian shrinkage regressions to Bayes classifier results in classifications comparable to some state-of-art methods.