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

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.

Bayesian nonparametric analysis for the detection of spikes in noisy calcium imaging data

“…For the autoregressive parameter γ, we use a Metropolis-Hastings within the Gibbs step. The sampling of A t exploits a combination of the nested slice sampler of Denti et al (2020) and of the telescoping sampler of Frühwirth-Schnatter et al (2020). A detailed description of the latter step is reported in the the Appendix.…”

“…The results attained by the proposed fCAM are compared to those obtained exploiting the common atom model (CAM) of Denti et al (2020) -which provides a benchmark for the clustering of the spikes and the stimulus-specific distributions -and the L 0 penalization method of Jewell et al (2019), which provides a benchmark for the task of spikes' detection. The latter method is tuned choosing the penalization parameter that minimizes the in-sample misclassification error rate, thus achieving a sort of oracle performance.…”

“…More specifically, our modeling framework estimates and clusters the distributions of the calcium transient spikes' amplitudes via a nested formulation of the generalized mixture of finite mixtures (gMFM) prior recently proposed by Frühwirth-Schnatter et al (2020). The proposed model further adopts the use of a common atom specification as in Denti et al (2020) for estimating the distribution of the spikes' amplitudes under each experimental condition. The proposed common atom gMFM has several advantages with respect to typical Bayesian nonparametric models for nested data.…”