Monte Carlo errors with less errors

By Ulli Wolff. 2003

299 citations recorded by the source corpus.

Abstract We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is argued to produce more certain error estimates than binning techniques and hence to help toward a better exploitation of expensive simulations. An effective integrated autocorrelation time is computed which is suitable to benchmark efficiencies of simulation algorithms with regard to specific observables of interest. A Matlab code is offered for download that implements the method. It can also combine independent runs (replica) allowing to judge their consistency.

View Paper: https://www.semanticscholar.org/paper/579f242b377eb224598ca2d94a116cb1093afe74

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Citations in the corpus

FLAG Review 2019 (2019, background): “In this scheme, nonperturbative and NLO running for the quark masses are shown to agree well from 100 GeV all the way down to 2 GeV [190].”
Review of lattice results concerning low-energy particle physics (2016, methodology): “These results are given in the MS scheme at 2GeV, which is standard nowadays, though some groups are starting to quote results at higher scales (e.g. Ref.”
Simulation of quantum circuits by low-rank stabilizer decompositions (2018, methodology): “Error bars represent the statistical error estimated using the MATLAB code due to Wolff [58] (for estimating errors in Markov chain Monte Carlo data) (b) The number of stabilizer states k used by the sum-over-Cliffords simulator was chosen as in Eq.”
ESPResSo - an extensible simulation package for research on soft matter systems (2006, unknown): “The derivation of more abstract error estimates is supported by a simple linear regression, or, for correlated observables, the uwerr command, which calculates the errors of values derived by, in general, nonlinear functions from observables with known correlated errors [67].”