  The Event Horizon Telescope (EHT) is a millimeter-wavelength,
very-long-baseline interferometry (VLBI) experiment that is capable of
observing black holes with horizon-scale resolution. Early observations have
revealed variable horizon-scale emission in the Galactic Center black hole,
Sagittarius A* (Sgr A*). Comparing such observations to time-dependent general
relativistic magnetohydrodynamic (GRMHD) simulations requires statistical tools
that explicitly consider the variability in both the data and the models. We
develop here a Bayesian method to compare time-resolved simulation images to
variable VLBI data, in order to infer model parameters and perform model
comparisons. We use mock EHT data based on GRMHD simulations to explore the
robustness of this Bayesian method and contrast it to approaches that do not
consider the effects of variability. We find that time-independent models lead
to offset values of the inferred parameters with artificially reduced
uncertainties. Moreover, neglecting the variability in the data and the models
often leads to erroneous model selections. We finally apply our method to the
early EHT data on Sgr A*.
