Estimating errors reliably in Monte Carlo simulations of the Ehrenfest model

TL;DR

This paper explores the challenges of accurately estimating errors in Monte Carlo simulations of the Ehrenfest model, emphasizing the importance of accounting for correlations in samples to avoid misleading results.

Contribution

It introduces methods to obtain reliable error estimates from correlated samples in Markov chain Monte Carlo simulations of the Ehrenfest model.

Findings

Correlated sampling can mislead error perception.

Analytical and numerical methods improve error estimation.

Reliable error estimates are achievable despite correlations.

Abstract

Using the Ehrenfest urn model we illustrate the subtleties of error estimation in Monte Carlo simulations. We discuss how the smooth results of correlated sampling in Markov chains can fool one's perception of the accuracy of the data, and show (via numerical and analytical methods) how to obtain reliable error estimates from correlated samples.