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There is a growing interest in the estimation of the number of unseenfeatures, mostly driven by biological applications. A recent work brought out apeculiar property of the popular completely random measures (CRMs) as priormodels in Bayesian nonparametric (BNP) inference for the unseen-featuresproblem: for fixed prior's parameters, they all lead to a Poisson posteriordistribution for the number of unseen features, which depends on the samplinginformation only through the sample size. CRMs are thus not a flexible priormodel for the unseen-features problem and, while the Poisson posteriordistribution may be appealing for analytical tractability and ease ofinterpretability, its independence from the sampling information makes the BNPapproach a questionable oversimplification, with posterior inferences beingcompletely determined by the estimation of unknown prior's parameters. In thispaper, we introduce the stable-Beta scaled process (SB-SP) prior, and we showthat it allows to enrich the posterior distribution of the number of unseenfeatures arising under CRM priors, while maintaining its analyticaltractability and interpretability. That is, the SB-SP prior leads to a negativeBinomial posterior distribution, which depends on the sampling informationthrough the sample size and the number of distinct features, with correspondingestimates being simple, linear in the sampling information and computationallyefficient. We apply our BNP approach to synthetic data and to real cancergenomic data, showing that: i) it outperforms the most popular parametric andnonparametric competitors in terms of estimation accuracy; ii) it providesimproved coverage for the estimation with respect to a BNP approach under CRMpriors.

Scaled process priors for Bayesian nonparametric estimation of the unseen genetic variation