Abstract
This paper introduces the usage and performance of the R package tlrmvnmvt, aimed at computing high-dimensional multivariate normal and Student-t probabilities. The package implements the tile-low-rank methods with block reordering and the separationof-variable methods with univariate reordering. The performance is compared with two other state-of-the-art R packages, namely the mvtnorm and the TruncatedNormal packages. Our package has the best scalability and is likely to be the only option in thousands of dimensions. However, for applications with high accuracy requirements, the TruncatedNormal package is more suitable. As an application example, we show that the excursion sets of a latent Gaussian random field can be computed with the tlrmvnmvt package without any model approximation and hence, the accuracy of the produced excursion sets is improved.
Highlights
The multivariate normal distribution (MVN) is probably the most well-known probability model due to its tractable analytical properties, principally being closed under conditioning and marginalization
We introduce tlrmvnmvt (Cao, Genton, Keyes, and Turkiyyah 2022), an R package that implements the methods introduced in Cao et al (2021) and that is available from the Comprehensive R Archive Network (CRAN) at https://CRAN.R-project.org/package=tlrmvnmvt, and compare the package with the two state-of-the-art alternatives, namely, the mvtnorm and the TruncatedNormal (Botev and Belzile 2019) packages, that implement the algorithms from Genz (1992) and from Botev (2017), respectively
We introduced the R package tlrmvnmvt that computes MVN/multivariate Student-t (MVT) probabilities with the TLR Monte Carlo methods described in Cao et al (2021)
Summary
The multivariate normal distribution (MVN) is probably the most well-known probability model due to its tractable analytical properties, principally being closed under conditioning and marginalization. 2 tlrmvnmvt: Low-Rank Methods for Multivariate Normal and t Probabilities in R dimensions Such examples include Bayes classification (Durante 2019), finding excursion and contour uncertainty regions (Bolin and Lindgren 2015), and maximum likelihood estimation (Cao, Genton, Keyes, and Turkiyyah 2021; Davison, Huser, and Thibaud 2013; Genton, Ma, and Sang 2011), among others. Because the TLR Monte Carlo method in Cao et al (2021) is based on Genz (1992), the tlrmvnmvt package includes an efficient implementation of the cumulative probability functions from the package mvtnorm.
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