A new reconstruction of multivariate normal orthant probabilities

By Peter S. Craig. 2007

53 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/83d660a7ae049bc6b1f125b0e1a856313794672f

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In Statistics and Probability

Citations in the corpus

Gaussian Copula Marginal Regression (2012, unknown): “[38] and Craig [9].”
The normal law under linear restrictions: simulation and estimation via minimax tilting (2016, methodology): “We note that initially we considered a comparison with other estimation schemes such as the radially symmetric approach of Nomura (2014a) and the specialized orthant probability algo-rithm of Miwa et al. (2003); Craig (2008); Nomura (2014b).”
A comparison of the maximum simulated likelihood and composite marginal likelihood estimation approaches in the context of the multivariate ordered-response model (2010, background): “Craig (2008) also alludes to this problem when he states that “(.”
The Composite Marginal Likelihood (CML) Inference Approach with Applications to Discrete and Mixed Dependent Variable Models (2014, methodology): “Craig (2008) also alludes to this problem when he states that “(...) the randomness that is inherent in such methods [referring to the Genz-Bretz algorithm (Genz and Bretz, 1999), but applicable in general to MSL methods] is sometimes more than a minor nuisance.””
The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models (2011, methodology): “This has led to several extensions of the MNL model through the relaxation of the independent and identically distributed (IID) error distribution (across alternatives) assumption.”