Browsing by Author "Jamodien, Riyaadh"

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    Data modelling & Bayesian model comparison with spherically symmetric priors
    (Stellenbosch : Stellenbosch University, 2020-12) Jamodien, Riyaadh; Eggers, H. C.; De Kock, M. B.; Kriel, Johannes N.; Stellenbosch University. Faculty of Science. Dept. of Physics.
    ENGLISH ABSTRACT: The analysis of data is common in many fields of science, and modelling data is one of the standard techniques in such analysis. Models are, of course, not unique and many theoretical models may be constructed to describe the same set of data. When considering many competing models, we naturally ask the question: which model best describes the data? It is well known that the chi-squared criterion, which is commonly cited as a goodness-offit between model and data, is inadequate as a measure of model quality. Rather, we employ the Bayesian framework of probability theory in addressing the question of model description of data. Within the Bayesian framework, the evidence (marginal likelihood) is the criterion by which to compare competing theoretical models. The evidence is an integral (over all parameter space) of the likelihood and prior. However, even for the simple case of linear models, there is no consensus or clarity on the choice of the best uninformative prior which enables the unbiased comparison of models with different numbers of parameters. In addressing the concern of the prior, we consider the framework of spherical symmetry, in which the evidence is reduced from an integral over a multi-dimensional space to that of a one-dimensional space, effectively reducing the problem to finding a single, optimal radial prior. We generalise existing results to a family of priors via scale relations in the form of a scaling parameter, of which several scaling relations are tested to find the best scale between models of different dimensions. We also introduce a new hyper-parameter, which had previously been conflated with model dimensions. With these developments we establish a prior that is sensitive to the new hyper-parameter, while insensitive to the model dimension, leading to the establishment of information criteria that are sensitive to these new parameters as well as the model dimension. These criteria are tested and shown to be an improvement over the existing body of work. These information criteria perform on par with widely accepted information criteria in the literature.