  There is a growing interest in the estimation of the number of unseen
features, mostly driven by biological applications. A recent work brought out a
peculiar property of the popular completely random measures (CRMs) as prior
models in Bayesian nonparametric (BNP) inference for the unseen-features
problem: for fixed prior's parameters, they all lead to a Poisson posterior
distribution for the number of unseen features, which depends on the sampling
information only through the sample size. CRMs are thus not a flexible prior
model for the unseen-features problem and, while the Poisson posterior
distribution may be appealing for analytical tractability and ease of
interpretability, its independence from the sampling information makes the BNP
approach a questionable oversimplification, with posterior inferences being
completely determined by the estimation of unknown prior's parameters. In this
paper, we introduce the stable-Beta scaled process (SB-SP) prior, and we show
that it allows to enrich the posterior distribution of the number of unseen
features arising under CRM priors, while maintaining its analytical
tractability and interpretability. That is, the SB-SP prior leads to a negative
Binomial posterior distribution, which depends on the sampling information
through the sample size and the number of distinct features, with corresponding
estimates being simple, linear in the sampling information and computationally
efficient. We apply our BNP approach to synthetic data and to real cancer
genomic data, showing that: i) it outperforms the most popular parametric and
nonparametric competitors in terms of estimation accuracy; ii) it provides
improved coverage for the estimation with respect to a BNP approach under CRM
priors.
