Predictive inference via Bayesian nonparametrics

Camerlenghi Federico, University of Milano Bicocca

H. Poincaré emphasized that a fundamental goal of science is prediction rather than the explanation of observed facts. This idea has been also pointed out by B. de Finetti, who wrote "science cannot limit itself to theorizing about accomplished facts but must foresee". The Bayesian nonparametric approach offers a natural probabilistic framework to address this fundamental issue through the notion of predictive distributions. In the present talk, we consider a population of animals composed of different species with unknown proportions, and we address prediction problems in this context. An archetypal problem in the species setting is the estimation of the unseen: given an initial observable sample from a population, how many new species will be observed in a future sample by the same population? While Bayesian nonparametric methods traditionally concentrate on abundance data, here we consider the scenario of incidence data, where the sampling unit is a plot and one records the incidence (presence or absence) of a species in the plot. We develop a new Bayesian nonparametric approach designed for incidence data, providing closed-form expression to address several prediction problems, including the estimation of unseen species and population size. Moreover, we consider similar issues in presence of multiple heterogeneous populations of species. We showcase the importance of our findings to face biodiversity estimation in a large variety of applied frameworks.

Area: CS9 - Bayesian Inference in Stochastic Processes (Alejandra Avalos-Pacheco)

Keywords: Bayesian nonparametrics; exchangeability; Prediction

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