Bayesian modeling of several covariance matrices and some results on propriety of the posterior for linear regression with correlated and/or heterogeneous errors

摘要

We explore simultaneous modeling of several covariance matrices across groups using the spectral (eigenvalue) decomposition and modified Cholesky decomposition We introduce several models for covariance matrices under different assumptions about the mean structure We consider dependence' matrices, which tend to have many parameters, as constant across groups and/or parsimoniously modeled via a regression formulation For variances, we consider both unrestricted across groups and more parsimoniously modeled via log-linear models In all these models we explore the propriety of the posterior when improper priors are used on the mean and 'variance parameters (and in some cases, on components of the 'dependence' matrices) The models examined include several common Bayesian regression models, whose propriety has not been previously explored, as special cases We propose a simple approach to weaken the assumption of constant dependence matrices in an automated fashion and describe how to compute Bayes factors to test the hypothesis of constant 'dependence' across groups The models are applied to data from two longitudinal clinical studies (C) 2005 Elsevier Inc All rights reserved.