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).