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Activity Number: 344
Type: Topic Contributed
Date/Time: Tuesday, August 2, 2016 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #318827
Title: Sparse Multidimensional Graphical Models: A Unified Bayesian Framework
Author(s): Yang Ni* and Francesco Stingo and Veera Baladandayuthapani
Companies: and MD Anderson Cancer Center and MD Anderson Cancer Center
Keywords: Directed acyclic graphs; ; Decomposable and non-decomposable graphs; ; LDL decomposition

Multi-dimensional data constituted by measurements along multiple axes have emerged across many scientific areas such as genomics and cancer surveillance. A common objective is to investigate the conditional dependencies among the variables along each axes taking into account multi-dimensional structure of the data. Traditional multivariate approaches are unsuitable for such highly structured data due to inefficiency, loss of power and lack of interpretability. In this paper, we propose a novel class of multi-dimensional graphical models based on matrix decompositions of the precision matrices along each dimension. Our approach is a unified framework applicable to both directed and undirected graphs as well as arbitrary combinations of these. Exploiting the marginalization of the likelihood, we develop efficient posterior sampling schemes based on partially collapsed Gibbs samplers. We illustrate our approaches through extensive simulations and an application in cancer surveillance.

Authors who are presenting talks have a * after their name.

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