Research Paper#Importance Sampling, Tilted Distributions, Rare Event Simulation🔬 ResearchAnalyzed: Jan 3, 2026 16:53
Limits of Weighted Empirical Approximations for Tilted Distributions
Published:Dec 30, 2025 04:30
•1 min read
•ArXiv
Analysis
This paper investigates the efficiency of a self-normalized importance sampler for approximating tilted distributions, which is crucial in fields like finance and climate science. The key contribution is a sharp characterization of the accuracy of this sampler, revealing a significant difference in sample requirements based on whether the underlying distribution is bounded or unbounded. This has implications for the practical application of importance sampling in various domains.
Key Takeaways
- •Provides a sharp characterization of the accuracy of a self-normalized importance sampler.
- •Highlights a significant difference in sample requirements based on the boundedness of the underlying distribution.
- •Findings are relevant to applications in finance, climate science, and rare event simulation.
Reference
“The findings reveal a surprising dichotomy: while the number of samples needed to accurately tilt a bounded random vector increases polynomially in the tilt amount, it increases at a super polynomial rate for unbounded distributions.”