Slice Monte Carlo Integration

2026-06-24

AI Summary

This work addresses the challenges of inefficient numerical integration and high estimator variance in Bayesian inference when dealing with expensive-to-evaluate target functions. To overcome these issues, the authors propose Slice Monte Carlo integration, a novel method that leverages a computationally inexpensive surrogate model to construct slice partitions inspired by nested sampling. Within each slice, samples are drawn from the prior distribution, enabling stratified Monte Carlo integration. The key innovation lies in decoupling slice volume estimation from target function evaluations, which facilitates adaptive, variance-aware allocation of computational resources. Empirical results on benchmark problems demonstrate that the proposed approach substantially improves both the accuracy of integral estimates and the efficiency of posterior sample generation.

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 (S$\ell$MC), a method that leverages a Nested Sampling-like procedure on the surrogate to partition the space into informative strata, or $\textit{slices}$, 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. A key advantage of S$\ell$MC is the decoupling of slice volume estimation from target function evaluation, which allows for adaptive, variance-aware allocation of computational effort. We investigate the properties of S$\ell$MC, demonstrate how to efficiently generate posterior samples, and validate the method on simple benchmark problems.

Problem

• numerical integration
• expensive target functions
• Bayesian inference
• surrogate models
• high variance

Innovation

• Slice Monte Carlo
• surrogate-assisted integration
• stratified sampling
• Nested Sampling
• variance-aware allocation