tokens: and GRMHD models, as well as from measurements of the ring diameter in the image domain. Our measurements remain consistent across methodologies, algorithms, data representations, and observed data sets. Motivated by the asymmetric emission ring structures seen in the reconstructed images (Section 5 ) and the similar emission structures seen in the images from GRMHD simulations (Section 6 ), we developed a family of geometric crescent models (see, e.g., Kamruddin Dexter 2013 ) to compare directly to the visibility data. We used two distinct Bayesian-inference algorithms and demonstrate that such crescent models are statistically preferred over other comparably complex geometric models that we have explored. We find that the crescent models provide fits to the data that are statistically comparable to those of the reconstructed images presented in Section 5 , allowing us to determine the basic parameters of the crescents. The best-fit models for the asymmetric emission ring have diameters of 43 ± 0.9 μ as and fractional widths relative to the diameter of 0.5. The emission drops sharply interior to the asymmetric emission ring with the central depression having a brightness 10% of the average brightness in the ring. The diameters of the geometric crescent models measure the characteristic sizes of the emitting regions that surround the shadows and not the sizes of the shadows themselves (see, e.g., Psaltis et al. 2015 ; Johannsen et al. 2016 ; Kuramochi et al. 2018 , for potential biases). We model the crescent angular diameter d in terms of the gravitational radius and distance, , as d = αθ g , where α is a function of spin, inclination, and R high ( α ≃ 9.6–10.4 corresponds to emission from the lensed photon ring only). We calibrate α by fitting the geometric crescent models to a large number of visibility data generated from the Image Library. We can also fit the model visibilities generated from the Image Library to the M87* data, which allows us to measure θ g directly. However, such a procedure is complicated by the stochastic nature of the emission in the accretion flow (see, e.g., Kim et al. 2016 ). To account for this turbulent structure, we developed a formalism and multiple algorithms that estimate the statistics of the stochastic components using ensembles of images from individual GRMHD simulations. We find that the visibility data are not inconsistent with being a realization of many of the GRMHD simulations. We conclude that the recovered model parameters are consistent across algorithms. Finally, we extract ring diameter, width, and shape directly from reconstructed images (see Section 5 ). The results are consistent with the parameter estimates from geometric crescent models. Following the same GRMHD calibration procedure, we infer values of θ g and α for regularized maximum likelihood and CLEAN reconstructed images. Combining results from all methods, we measure emission region diameters of 42 ± 3 μ as, angular sizes of
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