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Title: A hierarchical nonparametric approach for robust graphical modelling Authors:  Raffaele Argiento - Università Cattolica del Sacro Cuore (Italy) [presenting]
Abstract: Useful tools to express multivariate network structures in gene expression studies are graphical models. However, alternative models are needed when data are strongly overdisperse. An interesting proposal has been previously introduced which uses a Dirichlet process to cluster data-components and accommodate for overdispersion. We consider a more general class of nonparametric distributions, namely the class of normalised completely random measures (NormCRM), which yields a more flexible component clustering. Moreover, in order to borrow information across the data, we model the dependence among the NormCRM through a nonparametric hierarchical structure. At data level, each NormCRM is centred on the same base measure, which is a NormCRM itself. The discreteness of the shared base measure implies that the processes at data level share the same atoms. This desired feature allows to cluster together components of different data. We will compare the performances of the proposed model with competitors via a simulation study, moreover we will explore genomic expression patterns in the yeast Saccharomyces cerevisiae responding to diverse environmental transitions. We will identify the multivariate network structure of the data and meanwhile cluster components according their degree of over dispersion.