It is shown that an arbitrary joint partial derivative of the Bingham normalising constant, expressed in standard form, is proportional to the normalising constant of a Bingham distribution of higher dimension. Two consequences of this result are noted.

We present a unified approach to Laplace approximation of hypergeometric functions with two matrix arguments. The general form of the approximation is designed to exploit the Laplace approximations to hypergeometric functions of a single matrix argument presented in Butler and Wood (Ann....

From observed bid and ask prices of European call and put options we estimate the risk neutral density of a stock at some future time t gt; 0. We restrict attention to a class of densities with heavy tails and use a Bayesian formulation in order to study the variation in the distributions...