Accurate and consistent calculation of the mean and variance in Monte-Carlo simulations

TL;DR

This paper addresses the issue of reproducibility and accuracy in parallelized Monte-Carlo simulations by combining running mean and variance calculations with a robust summing algorithm to improve estimate reliability.

Contribution

It introduces a method that integrates accurate summing algorithms with running mean and variance calculations for more reliable Monte-Carlo results.

Findings

Enhanced accuracy of mean and variance estimates in parallel simulations

Reduced artificial randomness in Monte-Carlo results

Improved robustness and reproducibility of estimates

Abstract

In parallelized Monte-Carlo simulations, the order of summation is not always the same. When the mean is calculated in running fashion, this may create an artificial randomness in results which ought to be reproducible. This note takes a look at the problem and proposes to combine the running mean and variance algorithm with an accurate and robust summing algorithm in order to increase the accuracy and robustness of the Monte-Carlo estimates.