A Common Atoms Model for the Bayesian Nonparametric Analysis of Nested Data

• 成果类型: Article
• 署名作者: Denti, Francesco; Camerlenghi, Federico; Guindani, Michele; Mira, Antonietta
• 署名单位: University of California System; University of California Irvine; University of Milano-Bicocca; Universita della Svizzera Italiana; University of Insubria; University of Milano-Bicocca; Collegio Carlo Alberto; Bocconi University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.1933499
• 发表日期: 2023
• 页码: 405-416
• 关键词: dirichlet; mixtures

摘要

The use of large datasets for targeted therapeutic interventions requires new ways to characterize the heterogeneity observed across subgroups of a specific population. In particular, models for partially exchangeable data are needed for inference on nested datasets, where the observations are assumed to be organized in different units and some sharing of information is required to learn distinctive features of the units. In this manuscript, we propose a nested common atoms model (CAM) that is particularly suited for the analysis of nested datasets where the distributions of the units are expected to differ only over a small fraction of the observations sampled from each unit. The proposed CAM allows a two-layered clustering at the distributional and observational level and is amenable to scalable posterior inference through the use of a computationally efficient nested slice sampler algorithm. We further discuss how to extend the proposed modeling framework to handle discrete measurements, and we conduct posterior inference on a real microbiome dataset from a diet swap study to investigate how the alterations in intestinal microbiota composition are associated with different eating habits. We further investigate the performance of our model in capturing true distributional structures in the population by means of a simulation study.