Molinari, Marco;
(2020)
Bayesian inference for multiple Gaussian graphical models, with an application to the SABRE cohort study.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
The motivating application of this thesis is the Southall And Brent REvisited (SABRE) study, a tri-ethnic cohort study conducted in the UK. We analyse the metabolic and phenotypic data of SABRE, with a view to identifying potential ethnic differences in metabolite levels and associations, to gain a better understanding of different risk of cardio-metabolic disorders and diabetes development across ethnicities. Our first focus is on modelling the distribution of Homeostasis Model Assessment Insulin Resistance (HOMA IR), which is a frequent precursor to the development of type 2 diabetes. We adopt a Bayesian nonparametric random intercept/error model, which allows for data-driven clustering of patients, while adjusting for individual metabolite levels. The results highlight the presence of sub-populations in the data, with diverse levels of HOMA IR related to different metabolic profiles. The second stage of research is concerned with the development of Bayesian multiple graphical models, to infer the structure of association between metabolites, across ethnicities. In the first model we adopt a Dependent Generalised Dirichlet Process (DGDP) prior on the edge inclusion probabilities, allowing the estimation of multiple Gaussian Graphical Models (GGMs) in a sparse multivariate regression framework (i.e. the seemingly unrelated regression (SUR) model). The DGDP prior allows a convenient way to share information across edges and multiple graphs, while within the sparse SUR framework we impose sparsity on the precision matrices, through the Stochastic Search Structure Learning prior, and on the regression covariates, through the Horseshoe prior. In our final contribution, we propose a dynamic multiple groups extension of the Nodewise Regression technique. We allow multiple groups of different sample sizes to be analysed. We estimate dynamic multiple graphs adopting a dynamic shrinkage prior, which allows to share information across times and groups, while ensuring good computational scalability. Posterior inference is performed through Markov Chain Monte Carlo (MCMC).
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Bayesian inference for multiple Gaussian graphical models, with an application to the SABRE cohort study |
| Event: | UCL (University College London) |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2020. Original content in this thesis is licensed under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10097557 |
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