Given a multinomial decomposable graphical model, we identify several alternative parametrizations; in particular we consider conditional probabilities of clique-residuals given separators, as well as generalized log-odds-ratios. For each such parametrization, we construct the corresponding...

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...

Correlation coefficients have many applications for studying the relationship among multivariate observations. Classical inferences on correlation coefficients are mainly based on the normality assumption. This assumption is hardly realistic in the real world, which implies that the procedures...

Principal subspace theorems deal with the problem of finding subspaces supporting optimal approximations of multivariate distributions. The optimality criterion considered in this paper is the minimization of the mean squared distance between the given distribution and an approximating...

In this paper we define a class of skew-normal linear mixed measurement error models. This class provides a useful generalization of normal linear mixed models with measurement error in fixed effects variables. It is assumed that the random effects, model errors and measurement errors follow a...