In this paper, we study the problem of estimating the covariance matrix [Sigma] and the precision matrix [Omega] (the inverse of the covariance matrix) in a star-shape model with missing data. By considering a type of Cholesky decomposition of the precision matrix [Omega]=[Psi]'[Psi], where...

In this paper, we consider estimating the Cholesky decomposition (the lower triangular squared root) of the covariance matrix for a conditional independent normal model under four equivariant loss functions. Closed-form expressions of the maximum likelihood estimator and an unbiased estimator of...

The use of hierarchical Bayesian spatial models in the analysis of ecological data is increasingly prevalent. The implementation of these models has been heretofore limited to specifically written software that required extensive programming knowledge to create. The advent of WinBUGS provides...

This article considers the development of objective prior distributions for discrete parameter spaces. Formal approaches to such development—such as the <italic>reference prior</italic> approach—often result in a constant prior for a discrete parameter, which is questionable for problems that exhibit certain...

We propose a Bayesian stochastic search approach to selecting restrictions on multivariate regression models where the errors exhibit deterministic or stochastic conditional volatilities. We develop a Markov Chain Monte Carlo (MCMC) algorithm that generates posterior restrictions on the...