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- W2608872869 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 $mathcal{L}_2-$discrepancy. The optimal partitions are given by a textit{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." @default.
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- W2608872869 date "2017-04-18" @default.
- W2608872869 modified "2023-09-27" @default.
- W2608872869 title "Optimal Jittered Sampling for two Points in the Unit Square" @default.
- W2608872869 hasPublicationYear "2017" @default.
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