Dr Peter Craig, University of Durham

Multivariate normal orthant probabilities - geometry, computation and application to statistics

The multivariate normal distribution is the basic model for multivariate continuous variability and uncertainty and its properties are intrinsically interesting.  The orthant probablility (OP) is the probability that each component is positive and is of practical importance both as the generalisation of tail probability and as the likelihood function for multivariate probit models.  Efficient quasi-Monte Carlo methods are available for approximation of OPs but are unsuitable for high-precision calculations. However, accurate calculations are relatively straightforward for some covariance structures other than independence.  I shall present the geometry of two ways to express general OPs in terms of these simpler OPs, discuss the computational consequences and briefly illustrate the application of these methods to a classic application of multivariate probit modelling.