Latin hypercube sampling to reduce the variance in Monte Carlo integration: a practical guide and an application to gravitational-wave astronomy
Abstract
In applied statistics, likelihoods involving high-dimensional integrals are often approximated via Monte Carlo summation. Controlling the resulting numerical variance is crucial for reliable inference. We provide a practical introduction to Latin hypercube sampling (LHS) and its extension based on orthogonal arrays (OA-LHS) as strategies to reduce this variance by stratifying the sampling distribution. LHS asymptotically removes variance contributions from individual coordinates, while strength-2 OA-LHS also removes those from pairwise interactions, yielding orders-of-magnitude improvements over plain Monte Carlo estimators for suitable integrands. As a case study, we investigate their application to the selection function entering hierarchical inference of gravitational-wave populations. At approximately one million injections, we find only a marginal reduction in variance, with low statistical significance. Nevertheless, the computational cost of constructing these designs is negligible relative to evaluating gravitational-wave injections, making even marginal gains worth considering for future applications. This practical introduction to LHS and OA-LHS offers a starting point for other applications in physics and astronomy involving computationally expensive Monte Carlo calculations.
Related
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BibTeX
@misc{boschini2026latin,
title = {{Latin hypercube sampling to reduce the variance in Monte Carlo integration: a practical guide and an application to gravitational-wave astronomy}},
author = {Matteo Boschini and Davide Gerosa},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04045},
eprint = {2611.04045},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04045},
}
RIS
TY - UNPB
TI - Latin hypercube sampling to reduce the variance in Monte Carlo integration: a practical guide and an application to gravitational-wave astronomy
AU - Matteo Boschini
AU - Davide Gerosa
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.04045
UR - https://arxiv.org/abs/2611.04045
AB - In applied statistics, likelihoods involving high-dimensional integrals are often approximated via Monte Carlo summation. Controlling the resulting numerical variance is crucial for reliable inference. We provide a practical introduction to Latin hypercube sampling (LHS) and its extension based on orthogonal arrays (OA-LHS) as strategies to reduce this variance by stratifying the sampling distribution. LHS asymptotically removes variance contributions from individual coordinates, while strength-2 OA-LHS also removes those from pairwise interactions, yielding orders-of-magnitude improvements over plain Monte Carlo estimators for suitable integrands. As a case study, we investigate their application to the selection function entering hierarchical inference of gravitational-wave populations. At approximately one million injections, we find only a marginal reduction in variance, with low statistical significance. Nevertheless, the computational cost of constructing these designs is negligible relative to evaluating gravitational-wave injections, making even marginal gains worth considering for future applications. This practical introduction to LHS and OA-LHS offers a starting point for other applications in physics and astronomy involving computationally expensive Monte Carlo calculations.
ER -