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

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 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 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.