Identified vector autoregressive (VAR) models have become widely used on time series data in recent years, but finite sample inference for such models remains a challenge. In this study, we propose a conjugate prior for Bayesian analysis of normalized VAR models. Under the prior, the marginal...

With sparse structures and conditional independence, one could estimate the precision matrix of Gaussian graphical models more efficiently. Sun and Sun (2005) studied objective priors for star-shape graphical models. We consider a generative star-shape model. Objective priors such as invariance...

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...

In this paper, the reference prior is developed for a truncated model with boundaries of support as two functions of an unknown parameter. It generalizes the result obtained in a recent paper by Berger et al. (2009), in which a rigorous definition of reference priors was proposed and the prior...

The conditional autoregressive (CAR) and simultaneous autoregressive (SAR) models both have been used extensively for the analysis of spatial structure underlying lattice data in many areas, such as epidemiology, demographics, economics, and geography. Default Bayesian analyses have been...

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...