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A new reconstruction of multivariate normal orthant probabilities
Author(s) -
Craig Peter
Publication year - 2008
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2007.00625.x
Subject(s) - orthant , multivariate statistics , multivariate normal distribution , mathematics , matrix normal distribution , cumulative distribution function , elliptical distribution , matrix t distribution , statistics , probability density function
Summary. 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.