Advances in Bayesian Approaches for Directed and Undirected Graphical Models

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dc.contributor.advisorVannucci, Marinaen_US
dc.contributor.advisorPeterson, Christine B.en_US
dc.creatorOsborne, Nathanen_US
dc.date.accessioned2021-08-16T19:19:29Zen_US
dc.date.available2022-02-01T06:01:11Zen_US
dc.date.created2021-08en_US
dc.date.issued2021-08-05en_US
dc.date.submittedAugust 2021en_US
dc.date.updated2021-08-16T19:19:29Zen_US
dc.description.abstractIn recent years, there has been a growing interest in the use of graphical models to understand the dependence relationships among random variables. Graphical models can capture both directed and undirected relationships, which may arise from a variety of underlying distributions. This flexibility has made them applicable across many fields of study. In this thesis we advance the research on Bayesian methods for graphical model inference by providing novel approaches for both directed and undirected networks. We first introduce a simultaneous estimation approach for multiple Gaussian graphs that links the precision matrix entries across groups. This approach enables more accurate estimation and is accompanied by an efficient Gibbs sampling scheme. Next, we outline a Variational-EM algorithm for a Bayesian hierarchical model to estimate the latent network of compositional count data, while also selecting relevant external covariates. This model proves useful as we improve estimation of underlying networks while gaining insights into the effects of the covariates. Finally, we develop a multi-subject vector autoregression model with group level graph estimation and allow the cross-subject variance to be a function of covariates. We use variational inference for estimation and find that accounting for the cross-subject variance leads to more accurate group level edge selection. We illustrate these methods with applications to brain imaging and microbiome data.en_US
dc.embargo.terms2022-02-01en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationOsborne, Nathan. "Advances in Bayesian Approaches for Directed and Undirected Graphical Models." (2021) Diss., Rice University. <a href="https://hdl.handle.net/1911/111193">https://hdl.handle.net/1911/111193</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/111193en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectBayesian statisticsen_US
dc.subjectgraphical modelsen_US
dc.subjectvariational inferenceen_US
dc.titleAdvances in Bayesian Approaches for Directed and Undirected Graphical Modelsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentStatisticsen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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