|کد مقاله||کد نشریه||سال انتشار||مقاله انگلیسی||ترجمه فارسی||نسخه تمام متن|
|5129631||1489847||2018||7 صفحه PDF||سفارش دهید||دانلود کنید|
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