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

TL;DR

This work tackles the challenge of analyzing count‑compositional data that exhibit overdispersion, zeros (including structural zeros), and nonlinear covariate effects. The authors introduce two Bayesian nonparametric models, ZANIM‑BART and ZANIM‑LN‑BART, which extend the zero‑and‑N‑inflated multinomial (ZANIM) framework by placing independent BART priors on both the compositional probabilities and the structural zero probabilities, with ZANIM‑LN adding latent Gaussian random effects to capture extra dispersion and dependencies across categories. An efficient data‑augmented MCMC algorithm combines ZANIM‑style augmentation with BART sampling routines, enabling flexible, nonlinear covariate effects to be learned without prespecifying functional forms. Through simulations, the method demonstrates strong recovery of nonlinear covariate effects and structural zeros and outperforms competing approaches such as ZIDM‑reg and multinomial‑BART, particularly under misspecification. Real data applications to human gut microbiome and modern pollen–climate data illustrate improved model fit (e.g., lower WAIC, better marginal ECDF matches) and richer inferential outputs, including covariate effects on both the compositional and structural zero components and, in the LN variant, latent correlations among taxa. Overall, the approach offers a principled and scalable framework for zero‑inflated count‑compositional data with complex covariate relationships, with broad applicability in microbiome and palaeoclimate research.

Abstract

Count-compositional data arise in many different fields, including high-throughput microbiome sequencing and palynology experiments, 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 nonlinear covariate effects. To address these concerns, we propose 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 our 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 with two case studies in microbiome and palaeoclimate modelling.

Figures (17)

• Figure 1: Comparison of the multinomial-BART, ZANIDM-reg and ZANIM-BART models in estimating the true compositional probabilities $\theta_{ij}$ (black solid lines) for $d=4$ categories. The posterior median and $95\%$ credible intervals are given in each case. The rugs along the $x$-axes represent samples where the observed counts are zero.
• Figure 2: ZANIDM-reg and ZANIM-BART estimates for the true zero-inflation probabilities $\zeta_{ij}$ (black solid lines) for $d=4$ categories. The posterior median and $95\%$ credible intervals are given in each case. The rugs along the $x$-axes represent samples where the observed counts are zero. Note that the multinomial-BART model is not included here as it does not include model components to capture zero-inflation.
• Figure 3: Traceplots of $\operatorname{KL}(\theta^{(t)})$ in Panel A and $\operatorname{KL}(\zeta^{(t)})$ in Panel B under the ZANIM-BART, ZANIM-LN-BART, and ZIDM-reg models, for a sample size of $n = 500$.
• Figure 4: Posterior predictive diagnostics for the ZANIM-BART, ZANIM-LN-BART, ZIDM-reg, and DM-reg models based on the marginal ECDF of the observed relative abundances, $y_{ij}/N_i$, for the Bacteroides and Prevotella taxa. The posterior predictive draws (grey lines) from the ZANIM-BART and ZANIM-LN-BART models closely follow the observed data (black lines), whereas the ZIDM-reg and DM-reg models fail to adequately capture the underlying patterns, particularly for the Bacteroides taxa. The rugs along the $x$-axes indicate the observed data.
• Figure 5: Marginal posterior probability of inclusion (MPPI) of the $d \times p = 2{,}716$ taxa/covariate pairs associated with the population-level count (Panel A) and zero-inflation Panel B) probabilities, estimated using the ZANIM-BART, ZANIM-BART-LN, ZIDM-reg, and DM-reg models. The indices on the $x$-axes are sorted in ascending order of MPPI to facilitate comparison across the models.