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We introduce a new Markov Chain Monte Carlo (MCMC) algorithm with paralleltempering for fitting theoretical models of horizon-scale images of black holesto the interferometric data from the Event Horizon Telescope (EHT). Thealgorithm implements forms of the noise distribution in the data that areaccurate for all signal-to-noise ratios. In addition to being triviallyparallelizable, the algorithm is optimized for high performance, achieving 1million MCMC chain steps in under 20 seconds on a single processor. We usesynthetic data for the 2017 EHT coverage of M87 that are generated based onanalytic as well as General Relativistic Magnetohydrodynamic (GRMHD) modelimages to explore several potential sources of biases in fitting models tosparse interferometric data. We demonstrate that a very small number of datapoints that lie near salient features of the interferometric data exertdisproportionate influence on the inferred model parameters. We also show thatthe preferred orientations of the EHT baselines introduce significant biases inthe inference of the orientation of the model images. Finally, we discussstrategies that help identify the presence and severity of such biases inrealistic applications.

Markov Chains for Horizons (MARCH). I. Identifying Biases in Fitting Theoretical Models to Event Horizon Telescope Observations