کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5129631 | 1489847 | 2018 | 7 صفحه PDF | دانلود رایگان |
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.
Journal: Statistics & Probability Letters - Volume 132, January 2018, Pages 55-61