Research Paper#Computational Geometry, Quasi-Monte Carlo Methods, Sampling🔬 ResearchAnalyzed: Jan 3, 2026 18:59
New Partition Method Improves Star Discrepancy
Published:Dec 29, 2025 09:39
•1 min read
•ArXiv
Analysis
This paper introduces a new method for partitioning space that leads to point sets with lower expected star discrepancy compared to existing methods like jittered sampling. This is significant because lower star discrepancy implies better uniformity and potentially improved performance in applications like numerical integration and quasi-Monte Carlo methods. The paper also provides improved upper bounds for the expected star discrepancy.
Key Takeaways
- •Introduces a new class of convex equivolume partition models.
- •Demonstrates that the new partition method yields lower expected star discrepancy than jittered sampling.
- •Provides improved upper bounds for the expected star discrepancy.
- •Resolves an open question regarding the strong partition principle for star discrepancy.
Reference
“The paper proves that the new partition sampling method yields stratified sampling point sets with lower expected star discrepancy than both classical jittered sampling and simple random sampling.”