Slice Monte Carlo Integration

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 textitslices, 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 SℓMC 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 SℓMC, demonstrate how to efficiently generate posterior samples, and validate the method on simple benchmark problems.