Bayesian model selection with applications to radio astronomy

Simple item page
dc.contributor.advisorBassett, Bruce Aen_ZA
dc.contributor.authorMootoovaloo, Arrykrishnaen_ZA
dc.date.accessioned2018-02-09T12:54:45Z
dc.date.available2018-02-09T12:54:45Z
dc.date.issued2017en_ZA
dc.description.abstractThis 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.en_ZA
dc.identifier.apacitationMootoovaloo, A. (2017). <i>Bayesian model selection with applications to radio astronomy</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Astronomy. Retrieved from http://hdl.handle.net/11427/27492en_ZA
dc.identifier.chicagocitationMootoovaloo, Arrykrishna. <i>"Bayesian model selection with applications to radio astronomy."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Astronomy, 2017. http://hdl.handle.net/11427/27492en_ZA
dc.identifier.citationMootoovaloo, A. 2017. Bayesian model selection with applications to radio astronomy. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Mootoovaloo, Arrykrishna AB - 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. DA - 2017 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2017 T1 - Bayesian model selection with applications to radio astronomy TI - Bayesian model selection with applications to radio astronomy UR - http://hdl.handle.net/11427/27492 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/27492
dc.identifier.vancouvercitationMootoovaloo A. Bayesian model selection with applications to radio astronomy. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Astronomy, 2017 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/27492en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Astronomyen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherAstronomyen_ZA
dc.subject.otherCosmologyen_ZA
dc.titleBayesian model selection with applications to radio astronomyen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
thesis_sci_2017_mootoovaloo_arrykrishna.pdf
Size:
6.23 MB
Format:
Adobe Portable Document Format
Description:
Download
Collections
Masters