If X is a k-dimensional random vector, we denote by X(i,j) the vector X with coordinates i and j deleted. If for each i, j the conditional distribution of Xi, Xj given X(i,j) = x(i,j) is classical bivariate normal for each then it is shown that X has a classical k-variate normal distribution.

If X is a k-dimensional random vector, we denote by X(i) the vector X with coordinate i deleted and by X(i,j) the vector X with coordinates i and j deleted. If for each i the conditional distribution of Xi given X(i) = x(i) is univariate normal for each x(i) [there exists]K-1 and if for each i,...

A k-dimensional density function is determined by certain combinations of marginal and conditional densities. The present paper identifies all possible such specifications. Gelman and Speed (1993) have treated the finite discrete case of this problem. The present paper extends their work to a...