  Calibration precision is currently a limiting systematic in 21 cm cosmology
experiments. While there are innumerable calibration approaches, most can be
categorized as either `sky-based,' relying on an extremely accurate model of
astronomical foreground emission, or `redundant,' requiring a precisely regular
array with near-identical antenna response patterns. Both of these classes of
calibration are inflexible to the realities of interferometric measurement. In
practice, errors in the foreground model, antenna position offsets, and beam
response inhomogeneities degrade calibration performance and contaminate the
cosmological signal. Here we show that sky-based and redundant calibration can
be unified into a highly general and physically motivated calibration framework
based on a Bayesian statistical formalism. Our new framework includes sky and
redundant calibration as special cases but can additionally support relaxing
the rigid assumptions implicit in those approaches. Furthermore, we present
novel calibration techniques such as redundant calibration for arrays with no
redundant baselines, representing an alternative calibration method for imaging
arrays such as the MWA Phase I. These new calibration approaches could mitigate
systematics and reduce calibration error, thereby improving the precision of
cosmological measurements.
