The birth of the first luminous sources and the ensuing epoch of reionization are best studied via the redshifted 21-cm emission line , the signature of the first two imprinting the last .
In this work we present a fully-Bayesian method , hibayes , for extracting the faint , global ( sky-averaged ) 21-cm signal from the much brighter foreground emission .
We show that a simplified ( but plausible ) , Gaussian model of the 21-cm emission from the Cosmic Dawn epoch ( 15 \lesssim z \lesssim 30 ) , parameterized by an amplitude A _ { HI } , a frequency peak \nu _ { HI } and a width \sigma _ { HI } , can be extracted even in the presence of a structured foreground frequency spectrum ( parameterized as a 7 ^ { th } -order polynomial ) , provided sufficient signal-to-noise ( 400 hours of observation with a single dipole ) .
We apply our method to an early , 19-minute long observation from the Large aperture Experiment to detect the Dark Ages , constraining the 21-cm signal amplitude and width to be -890 < A _ { HI } < 0 mK and \sigma _ { HI } > 6.5 MHz ( corresponding to \Delta z > 1.9 at redshift z \simeq 20 ) respectively at the 95-per-cent confidence level in the range 13.2 < z < 27.4 ( 100 > \nu > 50 MHz ) .