Ensuring Robustness in Training Set Based Global 21-cm Cosmology
  Analysis
  We present a methodology for ensuring the robustness of our analysis pipeline
in separating the global 21-cm hydrogen cosmology signal from large systematics
based on singular value decomposition (SVD) of training sets. We show how
traditional goodness-of-fit metrics such as the $\chi^2$ statistic that assess
the fit to the full data may not be able to detect a suboptimal extraction of
the 21-cm signal when it is fit alongside one or more additional components due
to significant covariance between them. However, we find that comparing the
number of SVD eigenmodes for each component chosen by the pipeline for a given
fit to the distribution of eigenmodes chosen for synthetic data realizations
created from training set curves can detect when one or more of the training
sets is insufficient to optimally extract the signal. Furthermore, this test
can distinguish which training set (e.g. foreground, 21-cm signal) needs to be
modified in order to better describe the data and improve the quality of the
21-cm signal extraction. We also extend this goodness-of-fit testing to cases
where a prior distribution derived from the training sets is applied and find
that, in this case, the $\chi^2$ statistic as well as the recently introduced
$\psi^2$ statistic are able to detect inadequacies in the training sets due to
the increased restrictions imposed by the prior. Crucially, the tests described
in this paper can be performed when analyzing any type of observations with our
pipeline.
