Abstract:
This thesis consists of two main parts, both of which focus on Bayesian methods and the problem of model selection in particular. The first part investigates a new approach to computing the Bayes factor for model selection without needing to compute the Bayesian evidence, while the second part shows, through an analytical calculation of the Bayesian evidence, that Bayesian methods allow two point sources to be distinguished from a single point source at angular separations that are much smaller than the naive beam size at high signal to noise. In the first part, the idea is to create a supermodel by combining two models using a hyperparameter, which we call α. Setting α = 0 or 1 switches each of the models off. Hence, the ratio of the posterior of α at the two end points (0 or 1) gives the Bayes Factor. This effectively converts the problem of model selection into a Bayesian inference problem. One can then use a standard Markov Chain Monte Carlo method to map the posterior distribution of α and compute the Bayes factor. In the second part of this thesis, the Bayesian radio interferometry formalism of Lochner et al. (2015) is extended to take into account the gains of the antennae using the StEFCal algorithm, an important part of the calibration pipeline. Finally we study the case of a pair of sources and show that they can be resolved using an analytical computation of the Bayesian evidence. This demonstrates that Bayesian methods allow super-resolution: the pair of sources can be distinguished from a single source at arbitrarily small scales compared to the naive beam size, as long as the measurements have sufficient signal to noise.

Reference:
Mootoovaloo, A. 2017. Bayesian model selection with applications to radio astronomy. University of Cape Town.