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Detecting and characterizing the Epoch of Reionization and Cosmic Dawn viathe redshifted 21-cm hyperfine line of neutral hydrogen will revolutionize thestudy of the formation of the first stars, galaxies, black holes andintergalactic gas in the infant Universe. The wealth of information encoded inthis signal is, however, buried under foregrounds that are many orders ofmagnitude brighter. These must be removed accurately and precisely in order toreveal the feeble 21-cm signal. This requires not only the modeling of theGalactic and extra-galactic emission, but also of the often stochasticresiduals due to imperfect calibration of the data caused by ionospheric andinstrumental distortions. To stochastically model these effects, we introduce anew method based on `Gaussian Process Regression' (GPR) which is able tostatistically separate the 21-cm signal from most of the foregrounds and othercontaminants. Using simulated LOFAR-EoR data that include strong instrumentalmode-mixing, we show that this method is capable of recovering the 21-cm signalpower spectrum across the entire range $k = 0.07 - 0.3 \ \rm{h\, cMpc^{-1}}$.The GPR method is most optimal, having minimal and controllable impact on the21-cm signal, when the foregrounds are correlated on frequency scales $\gtrsim3$\,MHz and the rms of the signal has $\sigma_{\mathrm{21cm}} \gtrsim0.1\,\sigma_{\mathrm{noise}}$. This signal separation improves the 21-cmpower-spectrum sensitivity by a factor $\gtrsim 3$ compared to foregroundavoidance strategies and enables the sensitivity of current and future 21-cminstruments such as the {\sl Square Kilometre Array} to be fully exploited.

Statistical 21-cm Signal Separation via Gaussian Process Regression Analysis