Title: Understanding partially exchangeable nonparametric priors for discrete structures

Abstract: Species sampling models provide a general framework for random discrete distributions that are tailored for exchangeable data. However, they fall short when used for modeling heterogeneous data collected from related sources or distinct experimental conditions. To address this, partial exchangeability serves as the ideal probabilistic framework. While numerous models exist for partially exchangeable observations, a unifying framework, like species sampling models, is currently missing for this framework. Thus, we introduce multivariate species sampling models, a general class of models characterized by their partially exchangeable partition probability function. They encompass existing nonparametric models for partial exchangeable data, highlighting their core distributional properties. Our results allow the study of the induced dependence structure and facilitate the development of new models. This is a joint work with Beatrice Franzolini, Antonio Lijoi, and Igor Pruenster.

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