Multivariate species sampling models
Species sampling processes provide a general framework to study random discrete probability measures and are tailored for modeling statistical data that are assumed to be exchangeable. However, they fall short when used for heterogeneous data collected from distinct experimental conditions. In this setting, partial exchangeability can serves as the ideal probabilistic invariance condition for the observations. However, while a wealth of dependent processes have been studied for this setting, a unifying framework, similar to species sampling processes, is currently absent. To fill this gap, we introduce multivariate species sampling processes, which define a general class of models characterized by their partially exchangeable partition probability function. These models encompass existing nonparametric models for partial exchangeable data, thereby highlighting their core distributional properties and induced learning mechanisms. The results enable an in-depth comprehension of the induced dependence structure as well as facilitate the development of new models. This talk is based on joint works with Antonio Lijoi (Bocconi University), Igor Prünster (Bocconi University), and Giovanni Rebaudo (University of Torino).
Area: CS9 - Bayesian Inference in Stochastic Processes (Alejandra Avalos-Pacheco)
Keywords: Bayesian nonparametrics, partial exchangeability, random probability
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