In quantum Monte Carlo (QMC) methods, energy estimators are calculated as (functions of) statistical averages of quantities sampled during a calculation. Associated statistical errors of these averages are often estimated. This error estimation is not straightforward and there are several choices of the error estimation methods. We evaluate the performance of three methods (the Straatsma method, an autoregressive model, and a blocking analysis based on von Neumann's ratio test for randomness) for the energy time series given by three QMC methods [diffusion Monte Carlo, full configuration interaction Quantum Monte Carlo (FCIQMC), and coupled cluster Monte Carlo (CCMC)]. From these analyses, we describe a hybrid analysis method which provides reliable error estimates for a series of various lengths of FCIQMC and CCMC's time series. Equally important is the estimation of the appropriate start point of the equilibrated phase. We establish that a simple mean squared error rule method as described by White [K. P. White, Jr., Simulation 69(6), 323 (1997)] can provide reasonable estimations.

• Received 1 June 2021
• Accepted 10 March 2022

DOI:https://doi.org/10.1103/PhysRevE.105.045313

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

©2022 American Physical Society