  In order to study the "Cosmic Dawn" and the Epoch of Reionization with 21 cm
tomography, we need to statistically separate the cosmological signal from
foregrounds known to be orders of magnitude brighter. Over the last few years,
we have learned much about the role our telescopes play in creating a
putatively foreground-free region called the "EoR window." In this work, we
examine how an interferometer's effects can be taken into account in a way that
allows for the rigorous estimation of 21 cm power spectra from interferometric
maps while mitigating foreground contamination and thus increasing sensitivity.
This requires a precise understanding of the statistical relationship between
the maps we make and the underlying true sky. While some of these calculations
would be computationally infeasible if performed exactly, we explore several
well-controlled approximations that make mapmaking and the calculation of map
statistics much faster, especially for compact and highly redundant
interferometers designed specifically for 21 cm cosmology. We demonstrate the
utility of these methods and the parametrized trade-offs between accuracy and
speed using one such telescope, the upcoming Hydrogen Epoch of Reionization
Array, as a case study.
