Partitions for stratified sampling

François Clément, Nathan Kirk, Florian Pausinger*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

Classical jittered sampling partitions [0, 1]d into md cubes for a positive integer m and randomly places a point inside each of them, providing a point set of size N = md 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.

Original languageEnglish
Number of pages19
JournalMonte Carlo Methods and Applications
Early online date11 Jan 2024
DOIs
Publication statusEarly online date - 11 Jan 2024

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