Adaptive stratified monte carlo algorithm for numerical computation of integrals

TL;DR

This paper introduces an adaptive stratified Monte Carlo algorithm that improves numerical integral approximation by iteratively splitting strata based on variance indicators, enhancing efficiency.

Contribution

The paper presents a novel adaptive stratified sampling method that dynamically adjusts strata to reduce variance in Monte Carlo integration.

Findings

The proposed algorithm outperforms traditional Monte Carlo methods in numerical experiments.

Adaptive stratification significantly decreases variance and improves accuracy.

Numerical results confirm the efficiency of the adaptive approach.

Abstract

In this paper, we aim to compute numerical approximation integral by using an adaptive Monte Carlo algorithm. We propose a stratified sampling algorithm based on an iterative method which splits the strata following some quantities called indicators which indicate where the variance takes relative big values. The stratification method is based on the optimal allocation strategy in order to decrease the variance from iteration to another. Numerical experiments show and confirm the efficiency of our algorithm.