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Title: Mixtures of normalized nested compound random measures and their application Authors:  Riccardo Corradin - University of Nottingham (United Kingdom) [presenting]
Federico Camerlenghi - University of Milano-Bicocca (Italy)
Andrea Ongaro - University of Milano-Bicocca (Italy)
Abstract: Dependent random measures have been studied extensively over the past decades. Among the possible choices, a remarkable strategy to define a vector of dependent random measures is given by the family of compound random measures. We first provide a posterior characterization for vectors of normalized compound random measures, which allows us to perform efficient conditional posterior inference. Further, we embed a vector of compound random measures in a nested structure, obtaining a model which induces ties among different dimensions of the vector of random measures. As a byproduct, by convoluting a kernel function with these nested models, we can perform clustering of distributions and observations simultaneously. Upon a posterior representation of compound random measures, we can derive a conditional sampling strategy to perform conditional inference also for the nested case. Our studies are motivated by an ecological problem, where we aim to cluster provinces in Lombardy based on their distributions of the daily concentration of particulate matter, but also to properly quantify the risk of exceeding a threshold imposed by the European Union's regulations.