Bayesian constraints on the global 21-cm signal from the Cosmic Dawn
  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,
\textsc{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 $A_{\rm HI}$, a
frequency peak $\nu_{\rm HI}$ and a width $\sigma_{\rm HI}$, can be extracted
even in the presence of a structured foreground frequency spectrum
(parameterized as a $7^{\rm th}$-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 $-890 < A_{\rm HI} < 0$ mK and $\sigma_{\rm HI} > 6.5$ 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).
