Bayesian nonparametric models for zero-inflated count-compositional data using ensembles of regression trees

TL;DR

This paper introduces two Bayesian ensemble models using regression trees to effectively analyze zero-inflated count-compositional data, addressing overdispersion, excess zeros, and complex covariate effects.

Contribution

The authors develop novel Bayesian models with nonparametric priors and latent effects, improving flexibility and inference for zero-inflated compositional data.

Findings

Models successfully capture covariate effects in simulations.

Extension with latent effects models overdispersion and dependencies.

Case study demonstrates practical applicability in palaeoclimate data.

Abstract

Count-compositional data arise in many different fields, including high-throughput sequencing experiments, ecological surveys, and palaeoclimate studies, where a common, important goal is to understand how covariates relate to the observed compositions. Existing methods often fail to simultaneously address key challenges inherent in such data, namely: overdispersion, an excess of zeros, cross-sample heterogeneity, and complex covariate effects. To address these concerns, we propose two novel Bayesian models based on ensembles of regression trees. Specifically, we leverage the recently introduced zero-and-$N$-inflated multinomial distribution and assign independent nonparametric Bayesian additive regression tree (BART) priors to both the compositional and structural zero probability components of the model, to flexibly capture covariate effects. We further extend this by adding latent random effects to capture overdispersion and more general dependence structures among the categories. We develop an efficient inferential algorithm combining recent data augmentation schemes with established BART sampling routines. We evaluate our proposed models in simulation studies and illustrate their applicability through a case study of palaeoclimate modelling.