We analyse Very Long Baseline Interferometry (VLBI) observations of the blazar CGRaBS J0809+5341 using Bayesian inference methods. The observation was carried out at 5 GHz using 8 telescopes that form part of the European VLBI Network. Imaging and deconvolution using traditional methods imply that the blazar is unresolved. To search for source structure beyond the diffraction limit, we perform Bayesian model selection between three source models (point, elliptical Gaussian, and circular Gaussian). Our modelling jointly accounts for antenna-dependent gains and system equivalent flux densities. We obtain posterior distributions for the various source and instrumental parameters along with the corresponding uncertainties and correlations between them. We find that there is very strong evidence (>1e9 :1) in favour of elliptical Gaussian structure and using this model derive the apparent brightness temperature distribution of the blazar, accounting for uncertainties in the shape estimates. To test the integrity of our method, we also perform model selection on synthetic observations and use this to develop a Bayesian criterion for the minimum resolvable source size and consequently the maximum measurable brightness temperature for a given interferometer, dependent on the signal-to-noise ratio (SNR) of the data incorporating the aforementioned systematics. We find that calibration errors play an increasingly important role in determining the over-resolution limit for SNR>>100. We show that it is possible to exploit the resolving power of future VLBI arrays down to about 5 per cent of the size of the naturally-weighted restoring beam, if the gain calibration is precise to 1 per cent or less.
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