Radio Galaxy Shape Measurement with Hamiltonian Monte Carlo in the
  Visibility Domain
  Radio weak lensing, while a highly promising complementary probe to optical
weak lensing, will require incredible precision in the measurement of galaxy
shape parameters. In this paper, we extend the Bayesian Inference for Radio
Observations model fitting approach to measure galaxy shapes directly from
visibility data of radio continuum surveys, instead of from image data. We
apply a Hamiltonian Monte Carlo (HMC) technique for sampling the posterior,
which is more efficient than the standard Monte Carlo Markov Chain method when
dealing with a large dimensional parameter space. Adopting the exponential
profile for galaxy model fitting allows us to analytically calculate the
likelihood gradient required by HMC, allowing a faster and more accurate
sampling. The method is tested on SKA1-MID simulated observations at 1.4 GHz of
a field containing up to 1000 star-forming galaxies. It is also applied to a
simulated observation of the weak lensing precursor survey SuperCLASS. In both
cases we obtain reliable measurements of the galaxies' ellipticity and size for
all sources with SNR $\ge 10$, and we also find relationships between the
convergence properties of the HMC technique and some source parameters. Direct
shape measurement in the visibility domain achieves high accuracy at the
expected source number densities of the current and next SKA precursor
continuum surveys. The proposed method can be easily extended for the fitting
of other galaxy and scientific parameters, as well as simultaneously
marginalising over systematic and instrumental effects.
