Bayesian Modeling of Sequential Discoveries

• 成果类型: Article
• 署名作者: Zito, Alessandro; Rigon, Tommaso; Ovaskainen, Otso; Dunson, David B.
• 署名单位: Duke University; University of Milano-Bicocca; University of Jyvaskyla; University of Helsinki; Norwegian University of Science & Technology (NTNU)
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2060835
• 发表日期: 2023
• 页码: 2521-2532
• 关键词: species-accumulation functions; nonparametric-inference; Dirichlet process; number; probability; successes; sample; prediction; bounds; priors

摘要

We aim at modeling the appearance of distinct tags in a sequence of labeled objects. Common examples of this type of data include words in a corpus or distinct species in a sample. These sequential discoveries are often summarized via accumulation curves, which count the number of distinct entities observed in an increasingly large set of objects. We propose a novel Bayesian method for species sampling modeling by directly specifying the probability of a new discovery, therefore, allowing for flexible specifications. The asymptotic behavior and finite sample properties of such an approach are extensively studied. Interestingly, our enlarged class of sequential processes includes highly tractable special cases. We present a subclass of models characterized by appealing theoretical and computational properties, including one that shares the same discovery probability with the Dirichlet process. Moreover, due to strong connections with logistic regression models, the latter subclass can naturally account for covariates. We finally test our proposal on both synthetic and real data, with special emphasis on a large fungal biodiversity study in Finland. Supplementary materials for this article are available online.