A Common Atoms Model for the Bayesian Nonparametric Analysis of Nested Data
提出一种嵌套公共原子模型，用于分析嵌套数据中单元分布仅在少量观测上不同的情况，实现分布层和观测层的双层聚类，并通过高效切片采样算法进行可扩展后验推断，在饮食交换研究的微生物组数据中验证了模型效果。
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.