Discrepancy of stratified samples from partitions of the unit cube

Jittered sampling is a classical way of generating structured random sets in a d-dimensional unit cube. Such sets combine the simplicity of fixed grids with certain probabilistic properties of sets of i.i.d uniformly distributed points and are thus a popular choice in numerical integration. The discrepancy of a point set is a common measure for the irregularities of distribution and is directly linked to worst case approximation error in numerical integration.

In this talk, I extend the notion of jittered sampling to arbitrary partitions of the unit cube. This analysis has interesting connections to the Poisson-Binomial distribution which acts behind the scenes and is the main player in the proofs of our results. In the final part, I present recent results and applications of our methods.

This is joint work with Markus Kiderlen (Aarhus University), Nathan Kirk (U. Waterloo) and Stefan Steinerberger (U. Washington, Seattle).

Date:  2023-11-29
Start Time:   15:00
Speaker:  Florian Pausinger (Queen's Univ. Belfast, Northern Ireland)
Institution:  Queen's University of Belfast
Place:  Sala 5.5, DMUC
Research Groups: -Geometry
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