It is crucial to check validation of any statistical model after fitting it for a given set of data. In Bayesian statistics, a researcher can check the fit of the model using a variety of strategies. In this paper we consider two major aspects, first checking that the posterior inferences are...

Parameters in statistical problems often live in a geometry of certain shape. For example, count probabilities in a multinomial distribution belong to a simplex. For these problems, Bayesian analysis needs to model priors satisfying certain constraints imposed by the geometry. This paper...

The general class of complex elliptical shape distributions on a complex sphere provides a natural framework for modeling shapes in two dimensions. Such class includes many distributions, e.g., complex Normal, Watson, Bingham, angular central Gaussian and several others. We employ this class of...

Suppose a random vector X has a multinormal distribution with covariance matrix [Sigma] of the form [Sigma] = [Sigma]i=1k [theta]iMi, where Mi's form a known complete orthogonal set and [theta]i's are the distinct unknown eigenvalues of [Sigma]. The problem of estimation of [Sigma] is considered...

This paper proposes a general class of multivariate skew-elliptical distributions. We extend earlier results on the so-called multivariate skew-normal distribution. This family of distributions contains the multivariate normal, Student's t, exponential power, and Pearson type II, but with an...

This paper considers a new approach to develop a very general class of skew multivariate distributions. The approach is based on a linear combination of an elliptically distributed random variable with a linear constraint. Using this approach two different classes of multivariate distributions...

Let X1,..., Xp be p (= 3) independent random variables, where each Xi has a distribution belonging to the one-parameter exponential family of distributions. The problem is to estimate the unknown parameters simultaneously in the presence of extreme observations. C. Stein (Ann. Statist. 9 (1981),...