Partitions for stratified sampling

Clément François (), Kirk Nathan () and Pausinger Florian ()
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Clément François: Sorbonne Université, CNRS, LIP6, Paris, France
Kirk Nathan: Queen’s University Belfast, Belfast, United Kingdom
Pausinger Florian: Queen’s University Belfast, Belfast, United Kingdom

Monte Carlo Methods and Applications, 2024, vol. 30, issue 2, 163-181

Abstract: Classical jittered sampling partitions [ 0 , 1 ] d {[0,1]^{d}} into m d {m^{d}} cubes for a positive integer m and randomly places a point inside each of them, providing a point set of size N = m d {N=m^{d}} with small discrepancy. The aim of this note is to provide a construction of partitions that works for arbitrary N and improves straight-forward constructions. We show how to construct equivolume partitions of the d-dimensional unit cube with hyperplanes that are orthogonal to the main diagonal of the cube. We investigate the discrepancy of such point sets and optimise the expected discrepancy numerically by relaxing the equivolume constraint using different black-box optimisation techniques.

Keywords: Jittered sampling; stratified sampling (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1515/mcma-2023-2025

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