Error estimation and reduction with cross correlations

Abstract

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.

16 pages, RevTEX4, 4 figures, 6 tables, published version

References in corpus (3)

• Cross-correlations in scaling analyses of phase transitions
• Mean-value identities as an opportunity for Monte Carlo error reduction
• Zero-temperature phase of the XY spin glass in two dimensions: Genetic embedded matching heuristic

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