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

Peterlin, Jakob (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: multivariate normal integration, quasi-Monte Carlo, high-performance computing, Julia programming language, computational mathematics and numerical analysis
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: MF - Medicinska fakulteta
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2026
• Št. strani: 42 str.
• Številčenje: Vol. 41, art. 117
• PID: 20.500.12556/RUL-186233
• UDK: 519.6
• ISSN pri članku: 1613-9658
• DOI: 10.1007/s00180-026-01794-8
• COBISS.SI-ID: 288887043
• Datum objave v RUL: 28.08.2026

Gradivo je del revije

• Naslov: Computational statistics
• Skrajšan naslov: Comput. stat.
• Založnik: Springer Link
• ISSN: 1613-9658
• COBISS.SI-ID: 513648921

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: multivariatna normalna integracija, kvazi-Monte Carlo, visokozozmogljivo računalništvo, programski jezik Julia, statistična programska oprema

Projekti

• Financer: ARIS - Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
• Številka projekta: P3-0154
• Naslov: Metodologija za analizo podatkov v medicini