Formulating and critically examining the assumptions of global 21-cm
  signal analyses: How to avoid the false troughs that can appear in single
  spectrum fits
  The assumptions inherent to global 21-cm signal analyses are rarely
delineated. In this paper, we formulate a general list of suppositions
underlying a given claimed detection of the global 21-cm signal. Then, we
specify the form of these assumptions for two different analyses: 1) the one
performed by the EDGES team showing an absorption trough in brightness
temperature that they modeled separately from the sky foreground and 2) a new,
so-called Minimum Assumption Analysis (MAA), that makes the most conservative
assumptions possible for the signal. We show fits using the EDGES analysis on
various beam-weighted foreground simulations from the EDGES latitude with no
signal added. Depending on the beam used, these simulations produce large false
troughs due to the invalidity of the foreground model to describe the
combination of beam chromaticity and the shape of the Galactic plane in the
sky, the residuals of which are captured by the ad hoc flattened Gaussian
signal model. On the other hand, the MAA provides robust fits by including many
spectra at different time bins and allowing any possible 21-cm spectrum to be
modeled exactly. We present uncertainty levels and example signal
reconstructions found with the MAA for different numbers of time bins. With
enough time bins, one can determine the true 21-cm signal with the MAA to $<10$
times the noise level.
