Stratified Splitting for Efficient Monte Carlo Integration

The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as Bayesian inference, statistical physics, and machine learning. However, due to the curse of dimensionality, deterministic numerical methods are inefficient in high-dimensional settings. Consequentially, for many practical problems one must resort to Monte Carlo estimation. In this paper, we introduce a novel Sequential Monte Carlo technique called Stratified Splitting which enjoys a number of desirable properties not found in existing methods. Specifically, the method provides unbiased estimates and can handle various integrand types including indicator functions, which are used in rare-event probability estimation problems. Moreover, this algorithm achieves a rigorous efficiency guarantee in terms of the required sample size. The results of our numerical experiments suggest that the Stratified Splitting method is capable of delivering accurate results for a wide variety of integration problems.