Browsing by Author "Peterson, Christine B."

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    Advances in Bayesian Approaches for Directed and Undirected Graphical Models
    (2021-08-05) Osborne, Nathan; Vannucci, Marina; Peterson, Christine B.
    In 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.