  We introduce a new Markov Chain Monte Carlo (MCMC) algorithm with parallel
tempering for fitting theoretical models of horizon-scale images of black holes
to the interferometric data from the Event Horizon Telescope (EHT). The
algorithm implements forms of the noise distribution in the data that are
accurate for all signal-to-noise ratios. In addition to being trivially
parallelizable, the algorithm is optimized for high performance, achieving 1
million MCMC chain steps in under 20 seconds on a single processor. We use
synthetic data for the 2017 EHT coverage of M87 that are generated based on
analytic as well as General Relativistic Magnetohydrodynamic (GRMHD) model
images to explore several potential sources of biases in fitting models to
sparse interferometric data. We demonstrate that a very small number of data
points that lie near salient features of the interferometric data exert
disproportionate influence on the inferred model parameters. We also show that
the preferred orientations of the EHT baselines introduce significant biases in
the inference of the orientation of the model images. Finally, we discuss
strategies that help identify the presence and severity of such biases in
realistic applications.
