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

TL;DR

This paper introduces a nested Common Atoms Model (CAM) for Bayesian nonparametric analysis of hierarchical data, enabling efficient inference and clustering in complex nested datasets like microbiome studies.

Contribution

The paper presents a novel nested CAM that captures distributional differences across units with scalable inference, extending to discrete data and applied to microbiome analysis.

Findings

Effective in modeling nested data structures

Scalable inference with nested slice-sampler algorithm

Successfully applied to microbiome dataset

Abstract

The use of high-dimensional data 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.