Zero-inflated binary Tree Pólya splitting regression for multivariate count data

2026/01/21 by Fabrice Moudjieu, Jean Peyhardi, Maxime Réjou-Méchain +2 · 1 voice
Mathematics · #stat.AP

paper · pdf

Abstract

Species distribution models (SDMs) are widely used to assess the effects of environmental factors on species distributions. However, classical SDMs ignore inter-species dependencies. Multivariate SDMs (MSDMs), especially those based on latent Gaussian fields such as the multivariate Poisson log-normal (MPLN), address this limitation but face challenges related to computation, dimensionality, and interpretability. Pólya-splitting (PS) distributions offer an alternative, combining a model for total abundance with a multivariate allocation structure, and have natural interpretations from ecological process models. Yet, they lack flexibility in modeling correlation structures. Tree Pólya-splitting (TPS) distributions overcome this by introducing hierarchical structure such as a phylogenetic tree. In this paper, we extend TPS to account for zero-inflation, leading to the zero-inflated tree Pólya-splitting (Z-TPS) family. We detail its statistical properties, show how standard software enables efficient inference, and illustrate its ecological relevance using tree abundance data from over 180 genera across the Congo Basin tropical rainforest.

Citations

• Zero-inflation in the Multivariate Poisson Lognormal Family
• Tree Pólya Splitting distributions for multivariate count data
• Asymptotic tail properties of Poisson mixture distributions
• Variational inference for sparse network reconstruction from count data
• Splitting models for multivariate count data
• A Review of Multivariate Distributions for Count Data Derived from the Poisson Distribution
• Variable selection for sparse Dirichlet-multinomial regression with an application to microbiome data analysis
• Generalized Additive Models for Location, Scale and Shape
• Analysis of multivariate probit models
• Changes in Plant Community Diversity and Floristic Composition on Environmental and Geographical Gradients

Discussions

• Zero-inflated binary Tree Pólya splitting regression for multivariate count data https://arxiv.org/abs/2601.14815v1 [bsky, 0 points, 0 comments]

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