Doubly blocked variant of Genz’s method for multivariate normal integration

Peterlin, Jakob (author)

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.

• Language: English
• Keywords: multivariate normal integration, quasi-Monte Carlo, high-performance computing, Julia programming language, computational mathematics and numerical analysis
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: MF - Faculty of Medicine
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: 42 str.
• Numbering: Vol. 41, art. 117
• PID: 20.500.12556/RUL-186233
• UDC: 519.6
• ISSN on article: 1613-9658
• DOI: 10.1007/s00180-026-01794-8
• COBISS.SI-ID: 288887043
• Publication date in RUL: 28.08.2026

Record is a part of a journal

• Title: Computational statistics
• Shortened title: Comput. stat.
• Publisher: Springer Link
• ISSN: 1613-9658
• COBISS.SI-ID: 513648921

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: multivariatna normalna integracija, kvazi-Monte Carlo, visokozozmogljivo računalništvo, programski jezik Julia, statistična programska oprema

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P3-0154
• Name: Metodologija za analizo podatkov v medicini