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Optimal Jittered Sampling for two points in the unit square

Author

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  • Pausinger, Florian
  • Rachh, Manas
  • Steinerberger, Stefan

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.

Suggested Citation

  • Pausinger, Florian & Rachh, Manas & Steinerberger, Stefan, 2018. "Optimal Jittered Sampling for two points in the unit square," Statistics & Probability Letters, Elsevier, vol. 132(C), pages 55-61.
    • Handle: RePEc:eee:stapro:v:132:y:2018:i:c:p:55-61
    DOI: 10.1016/j.spl.2017.09.010
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