Statistics of biophysical signal characteristics and state specificity of the human EEG

The analysis of records of biophysical signals like EEG have become increasingly interesting to physicists since the development of new algorithms for time-series analysis. This analysis, however, requires both—an adequate methodology assessing the time-series characteristics and an appropriate statistical assessment of the measures resulting from these algorithms. The latter should separate inherent effects from those appearing only by chance, .e.g., in terms of an appropriate test statistics. As a step towards such a statistical assessment we present here a data resampling approach: Data resampling techniques allow for the estimation of the variance of an F-value as obtained through variance analysis. A test statistics based on the so-called F-ratio σ2(F)/F2 is derived and the simulation of outcomes allows for the determination of its quantiles. A multivariate formulation allows for the simultaneous inclusion of linear and nonlinear time-series measures into the analysis. We applied these concepts to the problem of distinguishing EEG of healthy probands from the EEG of patients diagnosed as schizophrenic. Together with an approach involving Bayes formula to weight the variables, it reveals a reliable discriminance performance of 81% when the nonlinear measure χ and the linear measures δ- and α-power are included.