Novel Statistical Framework for Modeling Systematics in Global 21-cm Cosmology

Currently, the Dark Ages and Cosmic Dawn epochs represent essentially unexplored frontiers for our understanding of the Universe, with a vast discovery potential for both new astrophysics and physics. Based on our full data analysis pipeline to extract the sky-averaged, primordial neutral Hydrogen signal from 21-cm observations, we are developing a rigorous statistical framework to determine the validity of the training sets we employ to model systematics, for many of which we have limited absolute knowledge due to difficulties either measuring or characterizing them. Even in a lunar farside environment free of terrestrial radio contamination and a relevant ionosphere, such as that for the Dark Ages Polarimeter PathfindER (DAPPER) mission concept, systematics include uncertainties affecting the description of the intrinsic foreground, the antenna beam, the horizon, and at least extent a well-characterized receiver. In order to evaluate these model characteristics separately from those of the signal, we first utilize a minimum assumption analysis that allows us to constrain and determine the goodness-of-fit of the systematics independently. A principal component analysis modeling each of the systematics, with prior weights determined by the eigenvalues that establish mode importance with respect to the noise level, leads to a fitting evaluation that can subsequently be repeated while iteratively adjusting the model until an acceptable fit and level of error are achieved. This yields a covariance matrix of the systematics that can then be fully incorporated into a nonlinear fit of a chosen signal model to start a similar, independent iterative process to obtain a good fit for the signal. Examples of this methodology will be presented here, as well as in companion presentations, demonstrating the power of this approach for ongoing and upcoming global 21-cm studies.