  We propose a probabilistic framework for performing simultaneous estimation
of source structure and fringe-fitting parameters in Very Long Baseline
Interferometry (VLBI) observations. As a first step, we demonstrate this
technique through the analysis of synthetic short-duration Event Horizon
Telescope (EHT) observations of various geometric source models at 230 GHz, in
the presence of baseline-dependent thermal noise. We perform Bayesian parameter
estimation and model selection between the different source models to obtain
reliable uncertainty estimates and correlations between various source and
fringe-fitting related model parameters. We also compare the Bayesian
posteriors with those obtained using widely-used VLBI data reduction packages
such as CASA and AIPS, by fringe-fitting 200 Monte Carlo simulations of each
source model with different noise realisations, to obtain distributions of the
Maximum A Posteriori (MAP) estimates. We find that, in the presence of resolved
asymmetric source structure and a given array geometry, the traditional
practice of fringe-fitting with a point source model yields appreciable offsets
in the estimated phase residuals, potentially biasing or limiting the dynamic
range of the starting model used for self-calibration. Simultaneously
estimating the source structure earlier in the calibration process with formal
uncertainties improves the precision and accuracy of fringe-fitting and
establishes the potential of the available data especially when there is little
prior information. We also note the potential applications of this method to
astrometry and geodesy for specific science cases and the planned improvements
to the computational performance and analyses of more complex source
distributions.
