  Observations with radio arrays that target the 21-cm signal originating from
the early Universe suffer from a variety of systematic effects. An important
class of these are reflections and spurious couplings between antennas. We
apply a Hamiltonian Monte Carlo sampler to the modelling and mitigation of
these systematics in simulated Hydrogen Epoch of Reionisation Array (HERA)
data. This method allows us to form statistical uncertainty estimates for both
our models and the recovered visibilities, which is an important ingredient in
establishing robust upper limits on the Epoch of Reionisation (EoR) power
spectrum. In cases where the noise is large compared to the EoR signal, this
approach can constrain the systematics well enough to mitigate them down to the
noise level for both systematics studied. Where the noise is smaller than the
EoR, our modelling can mitigate the majority of the reflections with there
being only a minor level of residual systematics, while cross-coupling sees
essentially complete mitigation. Our approach performs similarly to existing
filtering/fitting techniques used in the HERA pipeline, but with the added
benefit of rigorously propagating uncertainties. In all cases it does not
significantly attenuate the underlying signal.
