Statistics and Biostatistics seminar series
Nathan Kirk
Illinois Institute of Technology
Room: M3 3127
Quasi-Monte Carlo Methods and Combinatorial Discrepancy
Quasi-Monte Carlo (QMC) methods offer deterministic accuracy improvements over standard Monte Carlo sampling, but their classical error bound—given by the Koksma-Hlawka inequality and governed by the Hardy-Krause variation—often proves conservative in practice. In this talk, I present a recent randomized QMC framework that begins with ordinary random samples and partitions them into highly uniform point sets using tools from combinatorial discrepancy. The method introduces a new measure of smoothness, the smoothed-out variation, which captures cancellations ignored by the Hardy-Krause variation formulation and leads to a strictly tighter error bound. I’ll also show how the same construction extends naturally to weighted function spaces, producing sampling nodes that can be tuned to exploit known structure in the integrand.