Bayesian Analysis

Hierarchical Normalized Completely Random Measures for Robust Graphical Modeling

Andrea Cremaschi, Raffaele Argiento, Katherine Shoemaker, Christine Peterson, and Marina Vannucci

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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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Bayesian Anal., Advance publication (2018), 31 pages.

First available in Project Euclid: 28 March 2019

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

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Cremaschi, Andrea; Argiento, Raffaele; Shoemaker, Katherine; Peterson, Christine; Vannucci, Marina. Hierarchical Normalized Completely Random Measures for Robust Graphical Modeling. Bayesian Anal., advance publication, 28 March 2019. doi:10.1214/19-BA1153.

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Supplemental materials

  • Supplementary Material for “Hierarchical Normalized Completely Random Measures for Robust Graphical Modeling”. We include in this file additional theoretical justifications, details of the MCMC updates, as well as some additional results from the applications presented in the paper. Details on the features analysed in the radiomics case study are reported.