Jittered sampling is a classical way of generating structured random sets in a ddimensional 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 PoissonBinomial 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).
