A new reconstruction of multivariate normal orthant probabilities

Craig, Peter

Abstract

A new method is introduced for geometrically reconstructing orthant probabilities for non-singular multivariate normal distributions. Orthant probabilities are expressed in terms of those for auto-regressive sequences and an efficient method is developed for numerical approximation of the latter. The approach allows more efficient accurate evaluation of the multivariate normal cumulative distribution function than previously, for many situations where the original distribution arises from a graphical model. An implementation is available as a package for the statistical software R and an application is given to multivariate probit models.

Citation

Craig, P. (2008). A new reconstruction of multivariate normal orthant probabilities. Journal of the Royal Statistical Society: Series B, 70(1), 227-243. https://doi.org/10.1111/j.1467-9868.2007.00625.x

• Journal Article Type: Article
• Online Publication Date: Nov 2, 2007
• Publication Date: Feb 1, 2008
• Deposit Date: Feb 15, 2008
• Journal: Journal of the Royal Statistical Society: Series B
• Print ISSN: 1369-7412
• Electronic ISSN: 1467-9868
• Publisher: Royal Statistical Society
• Peer Reviewed: Peer Reviewed
• Volume: 70
• Issue: 1
• Pages: 227-243
• DOI: https://doi.org/10.1111/j.1467-9868.2007.00625.x
• Keywords: Multivariate normal distribution, Cumulative distribution function, Orthant probabilities, Polyhedral cones, Orthoscheme, Fractional fast Fourier transform, Multivariate probit model.
• Publisher URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9868.2007.00625.x