Tlrmvnmvt: Computing High-Dimensional Multivariate Normal and Student-t Probabilities with Low-Rank Methods in R

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 separation-of-variable methods with univariate reordering. The performance is compared with two other state-of-the-art R packages, namely the mvtnorm and the TruncatedNormal pack-ages. 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 Truncated-Normal 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. © 2022, American Statistical Association. All rights reserved.