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

Estimating errors reliably in Monte Carlo simulations of the Ehrenfest model