Title: Bayesian prediction with heterogeneous populations: An application to feature sampling
Authors: Federico Camerlenghi - University of Milano-Bicocca and Collegio Carlo Alberto (Italy) [presenting]
Abstract: The prediction of future outcomes of a random phenomenon is typically based on a certain number of analogous observations from the past. When observations come from multiple and heterogeneous populations, a natural notion of analogy is partial exchangeability and the problem of prediction can be effectively addressed in a Bayesian nonparametric setting. We define and investigate new classes of hierarchical processes which are useful for prediction in species sampling and feature models. We concentrate our attention on feature models, which generalize species sampling models by allowing every observation to belong to more than one species, now called features. In this setting we are able to forecast the outcome of additional samples having arbitrary size and to derive distributional properties for many statistics of interest, such as the number of hitherto unseen features that will be observed in an additional sample.