Monte Carlo errors with less errors

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.

arXiv comment22 pages, 4 figures, link-address for software download, V4: Improvement in eq.(58) and (42) for error of tau_int => new version of software.Only subleading error terms affected, results should remain compatible

References in corpus (1)

• Comparative Benchmarks of full QCD Algorithms

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