Slice Monte Carlo Integration
Abstract
Numerical integration involving expensive target functions is a common bottleneck in Bayesian inference and simulation. When a cheap surrogate is available, standard approaches such as reweighting or importance sampling often suffer from high variance and inefficient use of function evaluations. We introduce Slice Monte Carlo integration (SℓMC), a method that leverages a Nested Sampling-like procedure on the surrogate to partition the space into informative strata, or slices, while generating samples in the parameter space drawn from the prior within each slice. This enables stratified Monte Carlo integration of the expensive target function over the surrogate-induced partition, yielding an efficient estimate of the target integral. The surrogate level sets therefore make the induced ordering of the parameter space the relevant information for SℓMC, rather than the pointwise target-to-surrogate ratios governing importance-sampling efficiency. Another key advantage of SℓMC is the decoupling of slice volume estimation from the evaluation of the target, allowing the refinement of the slice-volume estimates without additional target evaluations. We investigate the properties of SℓMC, demonstrate how to efficiently generate posterior samples, and assess its robustness in controlled Gaussian benchmark families with continuously tunable surrogate-target mismatch.
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BibTeX
@misc{krondorfer2026slice,
title = {{Slice Monte Carlo Integration}},
author = {Johannes K. Krondorfer and Christian W. Binder and Matthias Neumann and Wolfgang von der Linden},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.25967},
eprint = {2606.25967},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.25967},
}
RIS
TY - UNPB
TI - Slice Monte Carlo Integration
AU - Johannes K. Krondorfer
AU - Christian W. Binder
AU - Matthias Neumann
AU - Wolfgang von der Linden
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2606.25967
UR - https://arxiv.org/abs/2606.25967
AB - Numerical integration involving expensive target functions is a common bottleneck in Bayesian inference and simulation. When a cheap surrogate is available, standard approaches such as reweighting or importance sampling often suffer from high variance and inefficient use of function evaluations. We introduce Slice Monte Carlo integration (SℓMC), a method that leverages a Nested Sampling-like procedure on the surrogate to partition the space into informative strata, or slices, while generating samples in the parameter space drawn from the prior within each slice. This enables stratified Monte Carlo integration of the expensive target function over the surrogate-induced partition, yielding an efficient estimate of the target integral. The surrogate level sets therefore make the induced ordering of the parameter space the relevant information for SℓMC, rather than the pointwise target-to-surrogate ratios governing importance-sampling efficiency. Another key advantage of SℓMC is the decoupling of slice volume estimation from the evaluation of the target, allowing the refinement of the slice-volume estimates without additional target evaluations. We investigate the properties of SℓMC, demonstrate how to efficiently generate posterior samples, and assess its robustness in controlled Gaussian benchmark families with continuously tunable surrogate-target mismatch.
ER -