tlrmvnmvt
Implementation of the classic Genz algorithm and a novel tile-low-rank algorithm for computing relatively high-dimensional multivariate normal and Student-t probabilities. For the Genz's algorithm (GenzBretz), we apply a univariate reordering preconditioner and for the tile-low-rank algorithms (TLRQMC), we apply a recursive block reordering preconditioner. The GenzBretz methods are different from their counterparts in the `mvtnorm` package in that the `tlrmvnmvt` package can accept any problem dimension and return the result in the log2 fashion, which is useful when the true probability is smaller than the machine precision. The TLRQMC algorithms can compute the probabilities up to tens of thousands of dimensions with the low-rank representation. However, this category of algorithms requires the existence of the low-rank property in the off-diagonal blocks of size m. The zorder function implements Morton's order in the 2D plane, which enhances the low-rank property of the produced covariance matrices.
Package functions: pmvn, pmvt, zorder
Cao, J., Genton, M. G., Keyes, D. E., & Turkiyyah, G. M. (2022), "tlrmvnmvt: Computing High-Dimensional Multivariate Normal and Student-t Probabilities with Low-Rank Methods in R," Journal of Statistical Software, 101.4, 1-25.