Optimal Monte Carlo method in estimating areas

Abstract

It is well known that Monte Carlo method can be used to estimate the area of a region which cannot be computed directly. There are a lot of ways to choose a larger region whose area is computable when one performs Monte Carlo method, but which region is the best? In this note, we find a best region in terms of fastest speed of convergence in probability, with the help of large deviations.

Keywords

• Monte Carlo method
• Hit-or-miss method
• Large deviations