We isolated the anomalous part of the cosmic electron-positron flux within a Bayesian likelihood analysis. Using 219 recent cosmic ray spectral data points, we inferred the values of selected cosmic ray propagation parameters. In the context of the propagation model coded in GalProp, we found a significant tension between the electron positron related and the rest of the fluxes. Interpreting this tension as the presence of an anomalous component in the electron-positron related data, we calculated background predictions for PAMELA and Fermi-LAT based on the non-electron-positron related fluxes. We found a deviation between the data and the predicted background even when uncertainties, including systematics, were taken into account. We identified this deviation with the anomalous electron-positron contribution. We briefly compared this model independent signal to some theoretical results predicting such an anomaly.