Monte-Carlo Integration on a Union of Polytopes

A new integration approach is presented that is tailored towards integrating over a union of polytopes with low coverage in high dimensions. It combines Markov Chain Monte Carlo and Multiphase Monte Carlo and takes advantage of the specific geometrical structure by directly sampling from it, which ensures scalability in higher dimensions. A feasibility study shows the efficiency of our method in comparison to the state-of-the-art approach GSL VEGAS. To showcase the specific strenght of the proposed method, integration is performed on a selected set of such multi-dimensional polytopes with low coverage.