Random density functions with common atoms and pairwise dependence

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

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.

Modelling ethnic differences in the distribution of insulin resistance via Bayesian nonparametric processes: an application to the SABRE cohort study

We analyse data from the Southall And Brent REvisited (SABRE) tri-ethnic study, where measurements of metabolic and anthropometric variables have been recorded. In particular, we focus on modelling the distribution of insulin resistance which is strongly associated with the development of type 2 diabetes. We propose the use of a Bayesian nonparametric prior to model the distribution of Homeostasis Model Assessment insulin resistance, as it allows for data-driven clustering of the observations. Anthropometric variables and metabolites concentrations are included as covariates in a regression framework. This strategy highlights the presence of sub-populations in the data, characterised by different levels of risk of developing type 2 diabetes across ethnicities. Posterior inference is performed through Markov Chains Monte Carlo (MCMC) methods.

Dependent generalized Dirichlet process priors for the analysis of acute lymphoblastic leukemia

We propose a novel Bayesian nonparametric process prior for modeling a collection of random discrete distributions. This process is defined by including a suitable Beta regression framework within a generalized Dirichlet process to induce dependence among the discrete random distributions. This strategy allows for covariate dependent clustering of the observations. Some advantages of the proposed approach include wide applicability, ease of interpretation, and availability of efficient MCMC algorithms. The motivation for this work is the study of the impact of asparginage metabolism on lipid levels in a group of pediatric patients treated for acute lymphoblastic leukemia.