This paper shows how to derive nonstationary spatio-temporal covariance functions via spatio-temporal stationary covariances and intrinsically stationary variograms. Three closely related kernels are employed for this purpose: 2{[phi](s1;t1)+[phi](s2;t2)}-[phi](s1+s2;t1+t2)-[phi](s1-s2;t1-t2),...

For a single observation X=x from a distribution having unknown location parameter [Theta], we investigate the behaviour of the posterior distribution as x varies, when the likelihood or the prior distribution is strongly unimodal. Extensions and generalizations of several results in the...

A stationary random field is often more complicated than a univariate stationary time series, since dependence for a random field extends in all directions, while there is only the natural distinction of past and future at any instant in a univariate time series. In this paper we start from a...

For the multivariate log-concave distribution, it is shown that the hazard gradient is increasing in the sense of Johnson and Kotz. As an immediate consequence, the result of Gupta and Gupta (1997) on the multivariate normal hazard is obtained.

Let X[lambda]1,...,X[lambda]n be independent random variables such that X[lambda]i has exponential distribution with hazard rate [lambda]i, i=1,...,n. It is shown that [summation operator]i=1nX[lambda]i is more dispersed than [summation operator]i=1nX[lambda]i* if ([lambda]1,...,[lambda]n)...

Stationary covariance functions that model space-time interactions are in great demand. The goal of this paper is to introduce and develop new spatio-temporal stationary covariance models. Integral representations for covariance functions with certain properties, such as [alpha]-symmetry in the...