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A New Reconstruction of Multivariate Normal Orthant Probabilities
Abstract
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.
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“Even in low dimensions (d 7), the method compares favorably with highly specialized routines for orthant probabilities (Miwa et al., 2003;Craig, 2008).”
From The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting (2017) · cites this paper as Craig, 2008
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“Unfortunately, unless a special autoregressive covariance structure is present, these methods are hardly competitive in anything but very few dimensions.”
From The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting (2017) · cites this paper as Craig (2008)
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“This is a rare case for which the exact value of the probability is known, namely ℓ = 1/(d + 1), and decays very slowly to zero as d ↑ ∞.”
From The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting (2017) · cites this paper as Craig (2008)
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Citations
Cites
Numerical Computation of Multivariate Normal Probabilities
Genz, A. (1992) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.1992.10477010 · Cited by 1,020
The Evaluation of General Non-Centred Orthant Probabilities
Miwa, T., Hayter, A. J., & Kuriki, S. (2003) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/1467-9868.00382 · Cited by 100
Research works printed but not linked: 20
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Cited by
The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting
Botev, Z. I. (2017) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/rssb.12162 · Cited by 247
Metadata
- Authors
- Craig, P.
- Affiliations
- University of Durham , UK
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 2007-11-02
- Volume
- 70
- Issue
- 1
- Pages
- 227-243
- ISSN
- 1369-7412
- 1467-9868
- Cited by
- 39
- References
- 2
- Language
- en
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