Error estimation in the histogram Monte Carlo method

TL;DR

This paper analyzes various sources of error in the histogram Monte Carlo reweighting method, highlighting the significance of finite energy sampling range errors over correlations, and provides criteria for valid extrapolations.

Contribution

It identifies and quantifies additional error sources in histogram reweighting, especially the impact of finite energy sampling range, and offers guidelines for assessing extrapolation validity.

Findings

Finite energy sampling range can introduce significant errors.

Correlation effects are generally negligible compared to statistical errors.

Criteria are provided to determine the validity of histogram extrapolations.

Abstract

We examine the sources of error in the histogram reweighting method for Monte Carlo data analysis. We demonstrate that, in addition to the standard statistical error which has been studied elsewhere, there are two other sources of error, one arising through correlations in the reweighted samples, and one arising from the finite range of energies sampled by a simulation of finite length. We demonstrate that while the former correction is usually negligible by comparison with statistical fluctuations, the latter may not be, and give criteria for judging the range of validity of histogram extrapolations based on the size of this latter correction.