6533b861fe1ef96bd12c4d99

RESEARCH PRODUCT

Error estimation and reduction with cross correlations

Wolfhard JankeMartin Weigel

subject

Analysis of covarianceStatistical Mechanics (cond-mat.stat-mech)Monte Carlo methodHigh Energy Physics - Lattice (hep-lat)EstimatorFOS: Physical sciencesMarkov chain Monte CarloHybrid Monte Carlosymbols.namesakeHigh Energy Physics - LatticeResamplingStatisticssymbolsJackknife resamplingCondensed Matter - Statistical MechanicsMathematicsMonte Carlo molecular modeling

description

Besides the well-known effect of autocorrelations in time series of Monte Carlo simulation data resulting from the underlying Markov process, using the same data pool for computing various estimates entails additional cross correlations. This effect, if not properly taken into account, leads to systematically wrong error estimates for combined quantities. Using a straightforward recipe of data analysis employing the jackknife or similar resampling techniques, such problems can be avoided. In addition, a covariance analysis allows for the formulation of optimal estimators with often significantly reduced variance as compared to more conventional averages.

yearjournalcountryeditionlanguage
2010-02-24
https://dx.doi.org/10.48550/arxiv.1002.4517