Monte Carlo errors with less errors

TL;DR

This paper presents a detailed method for accurately estimating statistical errors in Monte Carlo simulations by analyzing autocorrelation functions, improving error assessment over traditional binning methods.

Contribution

It introduces a novel approach to estimate and sum autocorrelation functions for better error quantification and provides a Matlab implementation for practical use.

Findings

More reliable error estimates than binning techniques.

Effective autocorrelation time for benchmarking simulation efficiency.

Combines independent runs to assess consistency.

Abstract

We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is argued to produce more certain error estimates than binning techniques and hence to help toward a better exploitation of expensive simulations. An effective integrated autocorrelation time is computed which is suitable to benchmark efficiencies of simulation algorithms with regard to specific observables of interest. A Matlab code is offered for download that implements the method. It can also combine independent runs (replica) allowing to judge their consistency.