Making the most of data: Quantum Monte Carlo postanalysis revisited Article Swipe

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Tom Ichibha , Verena A. Neufeld , Kenta Hongo , Ryo Maezono , Alex J. W. Thom ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.1103/physreve.105.045313

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., ] can provide reasonable estimations.

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Monte Carlo method Estimator Quantum Monte Carlo Series (stratigraphy) Monte Carlo method in statistical physics Quasi-Monte Carlo method Statistical physics Monte Carlo integration Hybrid Monte Carlo Randomness Monte Carlo molecular modeling Computer science Dynamic Monte Carlo method Algorithm Mathematics Applied mathematics Statistics Markov chain Monte Carlo Physics Paleontology Biology

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Type: article
Language: en
Landing Page: https://doi.org/10.1103/physreve.105.045313
PDF: http://link.aps.org/pdf/10.1103/PhysRevE.105.045313
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Cited By: 1
References: 71
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DOI: https://doi.org/10.1103/physreve.105.045313

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Title: Making the most of data: Quantum Monte Carlo postanalysis revisited

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Language: en

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Publication year: 2022

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Publication date: 2022-04-19

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Authors: Tom Ichibha, Verena A. Neufeld, Kenta Hongo, Ryo Maezono, Alex J. W. Thom

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Landing page: https://doi.org/10.1103/physreve.105.045313

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Concepts: Monte Carlo method, Estimator, Quantum Monte Carlo, Series (stratigraphy), Monte Carlo method in statistical physics, Quasi-Monte Carlo method, Statistical physics, Monte Carlo integration, Hybrid Monte Carlo, Randomness, Monte Carlo molecular modeling, Computer science, Dynamic Monte Carlo method, Algorithm, Mathematics, Applied mathematics, Statistics, Markov chain Monte Carlo, Physics, Paleontology, Biology

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