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 (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.