Dirichlet Methods for Bayesian Source Detection in Radio Astronomy Images

The sheer volume of data to be produced by the next generation of radio telescopes—exabytes of data on hundreds of millions of objects—makes automated methods for the detection of astronomical objects ("sources") essential. Of particular importance are low surface brightness objects, which are not well found by current automated methods.  This thesis explores Bayesian methods for source detection that use Dirichlet or multinomial models for pixel intensity distributions in discretised radio astronomy images. A novel image discretisation method that incorporates uncertainty about how the image should be discretised is developed. Latent Dirichlet allocation — a method originally developed for inferring latent topics in document collections — is used to estimate source and background distributions in radio astronomy images. A new Dirichlet-multinomial ratio, indicating how well a region conforms to a well-specified model of background versus a loosely-specified model of foreground, is derived. Finally, latent Dirichlet allocation and the Dirichlet-multinomial ratio are combined for source detection in astronomical images.   The methods developed in this thesis perform source detection well in comparison to two widely-used source detection packages and, importantly, find dim sources not well found by other algorithms.