Efficient subsampling-rate selection for practical Multilevel Markov chain Monte Carlo
Abstract
The Multilevel Markov chain Monte Carlo algorithm accelerates Bayesian inversion by exploiting correlations between discretized quantities of interest across a hierarchy of model resolutions. A key practical parameter is the subsampling rate used to generate coarse-level proposals for the finer-level chains. Existing practice sets this rate equal to an integrated autocorrelation time as a proxy for proposal decorrelation, but this choice can be overly conservative and lead to substantial computational overhead. In this work we treat finite subsampling as an error-budget question. We derive a cost-error criterion for selecting a computationally efficient subsampling rate using estimates of sample variances, integrated autocorrelation times, and per-level costs. The criterion balances multilevel sampling errors across levels rather than enforcing approximate independence of the coarse proposals. We clarify the theoretical role of independence through an ideal reset-reference kernel, for which independent coarse proposals may be replaced by proposals generated from a reversible coarse-level kernel. We derive a Poisson-equation representation of the perturbation bias resulting from finite subsampling. Under a state-averaged lower-level forgetting assumption, this yields a conditional geometric perturbation-bias bound; in computation, the corresponding projected diagnostic is used as an empirical error-budget check. Numerical experiments on a highly autocorrelated elasticity beam benchmark show substantial reductions in computational cost compared with IAT-based subsampling. A second Darcy-flow inverse problem gives supporting evidence of qualitatively similar finite-subsampling behaviour in another elliptic benchmark.
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BibTeX
@misc{guilliams2026efficient,
title = {{Efficient subsampling-rate selection for practical Multilevel Markov chain Monte Carlo}},
author = {Lise Guilliams and Pieter Vanmechelen and Giovanni Samaey},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07956},
eprint = {2610.07956},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07956},
}
RIS
TY - UNPB
TI - Efficient subsampling-rate selection for practical Multilevel Markov chain Monte Carlo
AU - Lise Guilliams
AU - Pieter Vanmechelen
AU - Giovanni Samaey
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.07956
UR - https://arxiv.org/abs/2610.07956
AB - The Multilevel Markov chain Monte Carlo algorithm accelerates Bayesian inversion by exploiting correlations between discretized quantities of interest across a hierarchy of model resolutions. A key practical parameter is the subsampling rate used to generate coarse-level proposals for the finer-level chains. Existing practice sets this rate equal to an integrated autocorrelation time as a proxy for proposal decorrelation, but this choice can be overly conservative and lead to substantial computational overhead. In this work we treat finite subsampling as an error-budget question. We derive a cost-error criterion for selecting a computationally efficient subsampling rate using estimates of sample variances, integrated autocorrelation times, and per-level costs. The criterion balances multilevel sampling errors across levels rather than enforcing approximate independence of the coarse proposals. We clarify the theoretical role of independence through an ideal reset-reference kernel, for which independent coarse proposals may be replaced by proposals generated from a reversible coarse-level kernel. We derive a Poisson-equation representation of the perturbation bias resulting from finite subsampling. Under a state-averaged lower-level forgetting assumption, this yields a conditional geometric perturbation-bias bound; in computation, the corresponding projected diagnostic is used as an empirical error-budget check. Numerical experiments on a highly autocorrelated elasticity beam benchmark show substantial reductions in computational cost compared with IAT-based subsampling. A second Darcy-flow inverse problem gives supporting evidence of qualitatively similar finite-subsampling behaviour in another elliptic benchmark.
ER -