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Bayesian learning of regularized Gaussian graphical networks
Thesis (PhD (Mathematical Statistics))--University of Pretoria, 2024.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2024
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| _version_ | 1867613623880253440 |
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| access_status_str | Open Access |
| author2 | Arashi, Mohammad |
| author_browse | Arashi, Mohammad |
| author_facet | Arashi, Mohammad |
| collection | Thesis |
| dc_rights_str_mv | © 2023 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Thesis (PhD (Mathematical Statistics))--University of Pretoria, 2024. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/94178 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:39:05.758Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/94178 Bayesian learning of regularized Gaussian graphical networks Arashi, Mohammad u14016665@tuks.co.za Bekker, Andriette, 1958- Smith, Jarod Mark UCTD Bayesian shrinkage estimation Gaussian graphical model Block Gibbs sampler Differential network Precision matrix Sustainable Development Goals (SDGs) SDG-17: Partnerships for the goals Natural and Agricultural Science theses SDG-17 Thesis (PhD (Mathematical Statistics))--University of Pretoria, 2024. The advancement of digitisation in various scientific disciplines has generated data with numerous variables. Gaussian graphical models (GGMs) offer a convenient framework for analysing and interpreting the conditional relationships among these variables, with network inference relying on estimating the precision matrix within a multivariate Gaussian framework. Two novel Bayesian shrinkage methods are proposed for the estimation of the precision matrix. The first develops a Bayesian treatment of the frequentist alternative ridge precision estimator with the common l2 penalty, allowing for networks that are not necessarily highly sparse. The second caters for diverse sparsity by enabling both l1 and l2 based shrinkage within a naïve elastic net setting. Full block Gibbs samplers are provided for implementing the new estimators. The Bayesian graphical ridge and naïve elastic net priors are extended to allow for flexible shrinkage of the off-diagonal elements of the precision matrix. Simulations and practical case studies show that the proposed estimators compare favourably with competing methods and enrich methodological flexibility for data analysis. To this end, a Bayesian approach for estimating differential networks (DN), using the Bayesian adaptive graphical lasso, is introduced. Comparisons to state-of-the-art frequentist techniques highlight the utility of the proposed technique. The novel samplers considered are available in the ’baygel’ R package to facilitate usage and exploration for practitioners. Statistics PhD (Mathematical Statistics) Restricted Faculty of Natural and Agricultural Sciences 2024-01-31T06:35:20Z 2024-01-31T06:35:20Z 2024-05-14 2024 Thesis * A2024 http://hdl.handle.net/2263/94178 https://doi.org/10.25403/UPresearchdata.25111607 en © 2023 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | UCTD Bayesian shrinkage estimation Gaussian graphical model Block Gibbs sampler Differential network Precision matrix Sustainable Development Goals (SDGs) SDG-17: Partnerships for the goals Natural and Agricultural Science theses SDG-17 Bayesian learning of regularized Gaussian graphical networks |
| title | Bayesian learning of regularized Gaussian graphical networks |
| title_full | Bayesian learning of regularized Gaussian graphical networks |
| title_fullStr | Bayesian learning of regularized Gaussian graphical networks |
| title_full_unstemmed | Bayesian learning of regularized Gaussian graphical networks |
| title_short | Bayesian learning of regularized Gaussian graphical networks |
| title_sort | bayesian learning of regularized gaussian graphical networks |
| topic | UCTD Bayesian shrinkage estimation Gaussian graphical model Block Gibbs sampler Differential network Precision matrix Sustainable Development Goals (SDGs) SDG-17: Partnerships for the goals Natural and Agricultural Science theses SDG-17 |
| url | http://hdl.handle.net/2263/94178 https://doi.org/10.25403/UPresearchdata.25111607 |