  In this paper we present DMC, a model and associated tool for polarimetric
imaging of very long baseline interferometry datasets that simultaneously
reconstructs the full-Stokes emission structure along with the station-based
gain and leakage calibration terms. DMC formulates the imaging problem in terms
of posterior exploration, which is achieved using Hamiltonian Monte Carlo
sampling. The resulting posterior distribution provides a natural
quantification of uncertainty in both the image structure and in the data
calibration. We run DMC on both synthetic and real datasets, the results of
which demonstrate its ability to accurately recover both the image structure
and calibration quantities as well as to assess their corresponding
uncertainties. The framework underpinning DMC is flexible, and its specific
implementation is under continued development.
