Optimal Jittered Sampling for two points in the unit square

Florian Pausinger, Manas Rachh and Stefan Steinerberger

Statistics & Probability Letters, 2018, vol. 132, issue C, 55-61

Abstract: Jittered Sampling is a refinement of the classical Monte Carlo sampling method. Instead of picking n points randomly from [0,1]2, one partitions the unit square into n regions of equal measure and then chooses a point randomly from each partition. Currently, no good rules for how to partition the space are available. In this paper, we present a solution for the special case of subdividing the unit square by a decreasing function into two regions so as to minimize the expected squared L2-discrepancy. The optimal partitions are given by a highly nonlinear integral equation for which we determine an approximate solution. In particular, there is a break of symmetry and the optimal partition is not into two sets of equal measure. We hope this stimulates further interest in the construction of good partitions.

Keywords: Jittered Sampling; Calculus of variations; Numerical integration; Quasirandom point sets (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spl.2017.09.010

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