  Understanding how different classes are distributed in an unlabeled data set
is an important challenge for the calibration of probabilistic classifiers and
uncertainty quantification. Approaches like adjusted classify and count,
black-box shift estimators, and invariant ratio estimators use an auxiliary
(and potentially biased) black-box classifier trained on a different (shifted)
data set to estimate the class distribution and yield asymptotic guarantees
under weak assumptions. We demonstrate that all these algorithms are closely
related to the inference in a particular Bayesian model, approximating the
assumed ground-truth generative process. Then, we discuss an efficient Markov
Chain Monte Carlo sampling scheme for the introduced model and show an
asymptotic consistency guarantee in the large-data limit. We compare the
introduced model against the established point estimators in a variety of
scenarios, and show it is competitive, and in some cases superior, with the
state of the art.
