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December 2019 Hierarchical Normalized Completely Random Measures for Robust Graphical Modeling
Andrea Cremaschi, Raffaele Argiento, Katherine Shoemaker, Christine Peterson, Marina Vannucci
Bayesian Anal. 14(4): 1271-1301 (December 2019). DOI: 10.1214/19-BA1153

Abstract

Gaussian graphical models are useful tools for exploring network structures in multivariate normal data. In this paper we are interested in situations where data show departures from Gaussianity, therefore requiring alternative modeling distributions. The multivariate t-distribution, obtained by dividing each component of the data vector by a gamma random variable, is a straightforward generalization to accommodate deviations from normality such as heavy tails. Since different groups of variables may be contaminated to a different extent, Finegold and Drton (2014) introduced the Dirichlet t-distribution, where the divisors are clustered using a Dirichlet process. In this work, we consider a more general class of nonparametric distributions as the prior on the divisor terms, namely the class of normalized completely random measures (NormCRMs). To improve the effectiveness of the clustering, we propose modeling the dependence among the divisors through a nonparametric hierarchical structure, which allows for the sharing of parameters across the samples in the data set. This desirable feature enables us to cluster together different components of multivariate data in a parsimonious way. We demonstrate through simulations that this approach provides accurate graphical model inference, and apply it to a case study examining the dependence structure in radiomics data derived from The Cancer Imaging Atlas.

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Andrea Cremaschi. Raffaele Argiento. Katherine Shoemaker. Christine Peterson. Marina Vannucci. "Hierarchical Normalized Completely Random Measures for Robust Graphical Modeling." Bayesian Anal. 14 (4) 1271 - 1301, December 2019. https://doi.org/10.1214/19-BA1153

Information

Published: December 2019
First available in Project Euclid: 28 March 2019

zbMATH: 1435.62121
MathSciNet: MR4044853
Digital Object Identifier: 10.1214/19-BA1153

Keywords: Bayesian nonparametrics , graphical models , hierarchical models , normalized completely random measures , radiomics data , t-distribution

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Vol.14 • No. 4 • December 2019
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