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

Area of Science:

• Statistical modeling
• Computational biology
• Bioinformatics

Background:

• Targeted therapeutic interventions require characterizing population subgroup heterogeneity.
• Partially exchangeable data models are needed for nested datasets with shared information.
• Existing models struggle with distinct features across nested data units.

Purpose of the Study:

• To propose a nested common atoms model (CAM) for analyzing nested datasets.
• To enable scalable posterior inference for complex data structures.
• To investigate associations between microbiota composition and eating habits.

Main Methods:

• Developed a nested common atoms model (CAM) for two-layered clustering (distributional and observational).
• Employed a computationally efficient nested slice sampler algorithm for scalable posterior inference.
• Extended the framework for discrete measurements and validated with a microbiome dataset and simulation study.

Main Results:

• The CAM effectively analyzes nested datasets where unit distributions differ slightly.
• Scalable posterior inference is achieved through the nested slice sampler.
• The model successfully identified associations between microbiota and diet in a real-world study.

Conclusions:

• The proposed nested common atoms model (CAM) offers a powerful tool for analyzing heterogeneous, nested data.
• The computational approach enables efficient inference on complex biological datasets.
• This framework advances our understanding of diet-microbiome interactions and supports targeted interventions.