Sufficientness Postulates for Generalized Indian Buffet Processes

Selecting a prior distribution is a fundamental problem of Bayesian inference, as well as one of the main critiques to 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 “sufficientness” postulates. We extend this characterization 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.