Scaled Process Priors for Bayesian Nonparametric Estimation of the Unseen Genetic Variation
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Scaled Process Priors for Bayesian Nonparametric Estimation of the Unseen Genetic Variation.pdf
Description
Published version
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3.89 MB
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Author(s)
Camerlenghi, Federico
Favaro, Stefano
Masoero, Lorenzo
Broderick, Tamara
Date Issued
September 29, 2022
Journal
Journal of the American Statistical Association
Publisher
Taylor & Francis
Citation
Camerlenghi, F., Favaro, S., Masoero, L., & Broderick, T. (2022). Scaled Process Priors for Bayesian Nonparametric Estimation of the Unseen Genetic Variation. Journal of the American Statistical Association, 119(545), 320–331. https://doi.org/10.1080/01621459.2022.2115918
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering
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DOI of Published Version
https://doi.org/10.1080/01621459.2022.2115918
