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Numerical evaluation of multinormal probabilities

Brodtkorb, Per Andreas LU (2004) In Preprint without journal information
Abstract
The multivariate normal probability integral with a product correlation structure can be transformed to a one dimensional integral and easily evaluated when the correlation matrix is non-singular and well conditioned. However, the nearly singular case is much more difficult and previous methods fail to compute it with high numerical precision. This paper demonstrates that the (nearly) singular case can be computed to almost double precision using a three step adaptive Simpson method with the epsilon-algorithm by Wynn (1956). Tests using randomly chosen problems show that the method gives more reliable results than the adaptive Simpson method of Dunnett (1989) as well as the globally adaptive integration routine DQAGPE from QUADPACK... (More)
The multivariate normal probability integral with a product correlation structure can be transformed to a one dimensional integral and easily evaluated when the correlation matrix is non-singular and well conditioned. However, the nearly singular case is much more difficult and previous methods fail to compute it with high numerical precision. This paper demonstrates that the (nearly) singular case can be computed to almost double precision using a three step adaptive Simpson method with the epsilon-algorithm by Wynn (1956). Tests using randomly chosen problems show that the method gives more reliable results than the adaptive Simpson method of Dunnett (1989) as well as the globally adaptive integration routine DQAGPE from QUADPACK

(Piessens et al., 1983). (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
unpublished
subject
in
Preprint without journal information
issue
2004:28
publisher
Manne Siegbahn Institute
ISSN
0348-7911
language
English
LU publication?
yes
id
80685b37-da66-4702-a4b4-5c354d05bca8 (old id 929324)
date added to LUP
2008-01-14 16:04:46
date last changed
2016-04-16 06:42:54
@misc{80685b37-da66-4702-a4b4-5c354d05bca8,
  abstract     = {The multivariate normal probability integral with a product correlation structure can be transformed to a one dimensional integral and easily evaluated when the correlation matrix is non-singular and well conditioned. However, the nearly singular case is much more difficult and previous methods fail to compute it with high numerical precision. This paper demonstrates that the (nearly) singular case can be computed to almost double precision using a three step adaptive Simpson method with the epsilon-algorithm by Wynn (1956). Tests using randomly chosen problems show that the method gives more reliable results than the adaptive Simpson method of Dunnett (1989) as well as the globally adaptive integration routine DQAGPE from QUADPACK <br/><br>
(Piessens et al., 1983).},
  author       = {Brodtkorb, Per Andreas},
  issn         = {0348-7911},
  language     = {eng},
  number       = {2004:28},
  publisher    = {ARRAY(0x9c1e3b0)},
  series       = {Preprint without journal information},
  title        = {Numerical evaluation of multinormal probabilities},
  year         = {2004},
}