Object-Oriented Zero-Information-Optimised Product of Monte Carlo Integrations

Abstract We propose an object-oriented Monte Carlo framework for computation of definite integrals with a primary focus on generality and simplicity, improving in find points existing software libraries. We introduce an optimised sampling method for a product of Monte Carlo integrations. The method does not require any a-priori knowledge of the integrands or the integration domains, and can be combined with other optimisation methods. Using our framework, we implement a naive uniform sampling method and the optimised one, and empirically compare them on the Monte Carlo computation of volumes of N-dimensional balls. The experiments confirm our theoretical expectations.