A Statistical Framework for Model Comparison in Particle Physics



Williams, Gareth
(2019) A Statistical Framework for Model Comparison in Particle Physics. PhD thesis, University of Liverpool.

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Abstract

With the vast quantities of data from experimental work an important task will be to distinguish which physical models are best fitted to these data sets especially in cases where the data shows deviations from the Standard Model. The Bayes factor is a tool used to determine which of two competing hypothe- ses is favoured given the data and in the case of model comparison provides the ability to determine which of the two physical model is favoured subject to the data. The marginalized likelihood is obtained by integrating the product of the likelihood P(D|θ⃗i) and the prior distribution of the parameters P(θ⃗1|Mi) over the parameter vectors θi for some model Mi given data D. Calculating the marginalized likelihood of two models and taking the ratio one obtains the Bayes factor. The degree to which one model is favoured over the other is obtained from a standard table which offers an interpretation of the result depending on which band of values the resultant Bayes factor lies. The computational framework to allow one to undertake statistical analysis of this kind is presented with a discussion on how it was built along with the underlying statistics to allow a user to input any model desired that they may wish to perform such analyses on. The minimally supersymmetric Standard Model and two-Higgs doublet model represent two of the simplest extensions to the Standard Model which both offer explanations to some of its deficiencies. Following the discussion on the fundamentals of these two models an explanation of how they handle the anomalous magnetic moment of the muon and lepton flavour violating decays is given and the Bayes factor calculated between these two models. The result of this indicates the two-Higgs doublet model is preferred given the data on these observables and the reasoning behind why such a result is obtained is presented in the final chapter of this thesis.

Item Type: Thesis (PhD)
Divisions: Faculty of Science and Engineering > School of Physical Sciences
Depositing User: Symplectic Admin
Date Deposited: 14 Aug 2020 11:25
Last Modified: 01 Sep 2022 07:21
DOI: 10.17638/03095440
Supervisors:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3095440