Numerical computation of rectangular bivariate and trivariate normal and t probabilities

By Alan Genz. Statistics and computing, 2004

310 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8f1b6f597b379bd8e15f6be8210c18c54443e361

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In Computational Mechanics

In Statistics and Probability

Citations in the corpus

Consistent inference in fixed-effects stochastic frontier models (2017, methodology): “…normal integrals, which makes problematic the extension of the Chen et al. (2014) approach to the heteroskedastic case, can be replaced by the approximation of ( T 2 ) 2-dimensional normal integrals whose evaluation has been shown to be accurate and computationally efficient (Genz, 2004).”
The Bivariate Normal Copula (2009, methodology): “Gupta (1963a) gives credit to Dunnett and Sobel (1955).”
Goodness‐of‐fit testing based on a weighted bootstrap: A fast large‐sample alternative to the parametric bootstrap (2012, methodology): “For N and T5, random number generation and the computation of the pdf and the cdf was performed using the excellent mvtnorm R package (Genz et al., 2011). For NC, GN, and T5N, the copula package (Kojadinovic & Yan, 2010) was used in addition. The results for dimension two are given in Table 2. The c”
Approximate Gaussian Integration using Expectation Propagation (2011, methodology): “es and Pollard, 1989), but the most ecient general, known method is numerical integration (Genz, 1992; Drezner and Wesolowsky, 1989; Drezner, 1994; Genz and Kwong, 2000; Genz and Brentz, 1999, 2002; Genz, 2004). A recent book (Genz and Bretz, 2009) gives a good overview. These algorithms make a seri”
FAST LARGE-SAMPLE GOODNESS-OF-FIT TESTS FOR COPULAS (2011, unknown): “The bivariate t generalization of the Plackett formula is given in Genz (2004): ∂tν,θ(x, y) ∂θ = ( 1 + (x2 + y2 − 2θxy)/(ν(1 − θ2)) )−ν/2 2π √ 1 − θ2 ,”
Quasi-Newton Methods: A New Direction (2012, background): “Fortunately, good, lightweight numerical approximations are available for this problem (Genz, 2004).”
The normal law under linear restrictions: simulation and estimation via minimax tilting (2016, methodology): “We first briefly describe the separation-of-variables (SOV) estimator of Genz (1992) (see also Geweke (1991)).”
Fast Probabilistic Optimization from Noisy Gradients (2013, background): “There are no analytic expressions for these integrals; but good (single precision), lightweight numerical approximations exist (Genz, 2004; Hennig & Kiefel, 2012).”
Towards Sharp Inapproximability For Any 2-CSP (2007, unknown): “For this, we use a MatLab implementation by Genz [19], based on the algorithm of [14] and improvements described in [20] for |ρ| close to 1.”
Maximizing acquisition functions for Bayesian optimization (2018, unknown): “low-dimensional multivariate normal CDF estimators [20, 21]).”
A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems (2017, methodology): “One can then use numerical methods [20, 21] to compute the multivariate normal cumulative distribution function and estimate the marginal probability:”