Hierarchical Normalized Completely Random Measures for Robust Graphical Modeling

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dc.citation.firstpage1271
dc.citation.issueNumber4
dc.citation.journalTitleBayesian Analysis
dc.citation.lastpage1301
dc.citation.volumeNumber14
dc.contributor.authorCremaschi, Andrea
dc.contributor.authorArgiento, Raffaele
dc.contributor.authorShoemaker, Katherine
dc.contributor.authorPeterson, Christine
dc.contributor.authorVannucci, Marina
dc.date.accessioned2021-10-06T14:15:18Z
dc.date.available2021-10-06T14:15:18Z
dc.date.issued2019
dc.description.abstractGaussian 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.
dc.identifier.citationCremaschi, Andrea, Argiento, Raffaele, Shoemaker, Katherine, et al.. "Hierarchical Normalized Completely Random Measures for Robust Graphical Modeling." <i>Bayesian Analysis,</i> 14, no. 4 (2019) Project Euclid: 1271-1301. https://doi.org/10.1214/19-BA1153.
dc.identifier.digital19-BA1153
dc.identifier.doihttps://doi.org/10.1214/19-BA1153
dc.identifier.urihttps://hdl.handle.net/1911/111440
dc.language.isoeng
dc.publisherProject Euclid
dc.rightsPublished under the terms of the Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.titleHierarchical Normalized Completely Random Measures for Robust Graphical Modeling
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpublisher version
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