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Updated: Jun 8, 2026

Basics of Multivariate Analysis in Neuroimaging Data
Published on: July 24, 2010
Error estimation and reduction with cross correlations
Martin Weigel1, Wolfhard Janke
1Theoretische Physik, Universität des Saarlandes, D-66041 Saarbrücken, Germany. weigel@uni-mainz.de
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.
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