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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 article, 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. Supplementary materials for this article are available online.

While the cost of sequencing genomes has decreased dramatically in recent years, this expense often remains nontrivial. Under a fixed budget, scientists face a natural trade-off between quantity and quality: spending resources to sequence a greater number of genomes or spending resources to sequence genomes with increased accuracy. Our goal is to find the optimal allocation of resources between quantity and quality. Optimizing resource allocation promises to reveal as many new variations in the genome as possible. We introduce a Bayesian nonparametric methodology to predict the number of new variants in a follow-up study based on a pilot study. When experimental conditions are kept constant between the pilot and follow-up, we find that our prediction is competitive with the best existing methods. Unlike current methods, though, our new method allows practitioners to change experimental conditions between the pilot and the follow-up. We demonstrate how this distinction allows our method to be used for more realistic predictions and for optimal allocation of a fixed budget between quality and quantity. We validate our method on cancer and human genomics data.