Predictive characterizations of feature allocation models

Beraha Mario, Politecnico di Milano

Selecting a prior distribution is a fundamental problem of Bayesian inference, as well as one of the main critiques of the Bayesian approach by other statisticians. Recent contributions proposed to sidestep prior selection by using a ``predictive approach'', whereby the statistician needs to assign a predictive rule for a new observation. In the context of species sampling methods, the interplay between classical (Bayesian) and predictive approaches is well understood in terms of W.E. Johnson's ``sufficientness'' postulates, which characterize the Dirichlet and Pitman-Yor processes in terms of their predictive distributions. We extend the investigation to feature sampling models, whereby each observation belongs to different groups, characterizing those priors for which the probability of discovery of new traits depends solely on the sample size and on the combination of sample size and total number of seen groups. Contrary to previous works on sufficientness postulates, our approach is analytical in nature. In particular, our results are based on a closed-form expression for the posterior distribution and two novel characterizations of point processes in terms of their reduced Palm kernels.

Area: IS2 - Dependence structures in Bayesian nonparametrics (Federico Camerlenghi)

Keywords: Bayesian nonparametrics; Point Processes; Palm Calculus