20.500.12556/RUL-186233 Doubly blocked variant of Genz’s method for multivariate normal integration High-dimensional multivariate normal (MVN) integration is a computational bottleneck in many statistical applications, particularly in finance and econometrics. This paper presents a modern, doubly blocked variant of Genz’s method for integrating MVN distributions, implemented in the Julia programming language. By leveraging multithreading, cache optimization, and SIMD/BLAS-friendly design, we address the memory bandwidth limitations of traditional implementations. We benchmark our approach against existing solvers in Julia, Fortran, and C++, demonstrating speedups that are often close to or above 100x over packages such as mvtnorm and tlrmvnmvt for large dimensions in the tested settings. We also compare our method with tiled low-rank approximations and apply it to a high-dimensional Gaussian copula model using real-world financial data. The results show that our implementation enables very fast probability calculations for high-dimensional portfolios, a task which was previously hard to achieve with standard tools. multivariate normal integration quasi-Monte Carlo high-performance computing Julia programming language computational mathematics and numerical analysis multivariatna normalna integracija kvazi-Monte Carlo visokozozmogljivo računalništvo programski jezik Julia statistična programska oprema true false true Angleški jezik Slovenski jezik Članek v reviji 2026-08-28 13:45:43 2026-08-28 13:45:50 2026-08-29 04:41:00 0000-00-00 00:00:00 2026 0 0 42 str. art. 117 Vol. 41 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.6 1613-9658 10.1007/s00180-026-01794-8 288887043 RAZ_Peterlin_Jakob_2026.pdf RAZ_Peterlin_Jakob_2026.pdf 1 4A4831468611ED79BFF91D8E9AE7DF9F e59602197edfbe0404b6f889e3dc16e1c0d8ef957c02bf0ea040e0590a5cff31 e873e764-a2d5-11f1-9b0d-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=245363 https://link.springer.com/article/10.1007/s00180-026-01794-8 0 da47ee3e-a2d5-11f1-9b0d-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=245362 Medicinska fakulteta 0 0 0