Numerical Computation of Multivariate Normal Probabilities

By Alan Genz. 1992

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Citations in the corpus

Counterfactual reasoning and learning systems: the example of computational advertising (2012, background): “Computing these probabilities amounts to integrating a multivariate Gaussian distribution (Genz, 1992).”
Nonlinear Statistical Learning with Truncated Gaussian Graphical Models (2016, methodology): “Multivariate in-tegrations in normal distributions have been well studied and many effective algorithms have been developed (Genz, 1992; Genz & Bretz, 2009).”
A skew item response model (2006, methodology): “This is important because there are several efficient algorithms for computing integrals related to the bivariate normal distribution (see Genz 1992, 1993).”
Further development of matrix-based system reliability method and applications to structural systems (2012, methodology): “…conditioned importance sampling (Ambartzumian et al. 1998), the product of conditional (marginal) cumulative distribution functions, so-called PCM methods (Pandey 1998, Yuan and Pandey 2006) and other approximation methods using transformation and conditional expectations (Genz 1992, Joe 1995).”
Quadratically gated mixture of experts for incomplete data classification (2007, methodology): “In the general case when M > 3, the results in (Genz, 1992) can be employed to perform the multiple integral numerically.”
Maximizing acquisition functions for Bayesian optimization (2018, background): “Below, we separately discuss each contribution along with its related literature.”
A new reconstruction of multivariate normal orthant probabilities (2007, methodology): “We have compared both reconstruction approaches with the random quasi-Monte Carlo algorithm QRSVN of Genz and Bretz (2002) as implemented in the mvtnorm package for R. Table 1 shows that both reconstruction approaches typically obtain an order of magnitude reduction in error by doubling computationa”
A solution to the stochastic unit commitment problem using chance constrained programming (2004, methodology): “Genz’s algorithm is known to be more accurate for the evaluation of tail probabilities.”
The evaluation of general non‐centred orthant probabilities (2003, methodology): “The value of e is used by Genz's procedure to stop the repetition (Genz, 1992).”
On the exact distribution of maximally selected rank statistics (2003, unknown): “However, for the known correlation matrix (% ij ), it is feasible to compute the probability P(−b 6 G 1 6 b; : : : ; −b 6 G N −1 6 b) with the procedure by Genz (1992).”
Excursion and contour uncertainty regions for latent Gaussian models (2012, methodology): “Using the transformation method by Genz (1992) on GMRF models is difficult without first inverting the precision matrix and then ignoring the sparsity of Q in the calculations.”