arXiv subjects

Frédéric Mortier

Publications and source records attributed to Frédéric Mortier.

5 recordsLinked to original sources

arXiv2026

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

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.

stat.AP↗

arXiv2025

Tree Pólya Splitting distributions for multivariate count data

In this article, we develop a new class of multivariate distributions adapted for count data, called Tree Pólya Splitting. This class results from the combination of a univariate distribution and singular multivariate distributions along a fixed partition tree. Known distributions, including the Dirichlet-multinomial, the generalized Dirichlet-multinomial and the Dirichlet-tree multinomial, are particular cases within this class. As we will demonstrate, these distributions are flexible, allowing for the modeling of complex dependence structures (positive, negative, or null) at the observation level. Specifically, we present the theoretical properties of Tree Pólya Splitting distributions by focusing primarily on marginal distributions, factorial moments, and dependence structures (covariance and correlations). A dataset of abundance of Trichoptera is used, on one hand, as a benchmark to illustrate the theoretical properties developed in this article, and on the other hand, to demonstrate the interest of these types of models, notably by comparing them to other approaches for fitting multivariate data, such as the Poisson-lognormal model in ecology or singular multivariate distributions used in microbiome.

math.ST↗

arXiv2023

Asymptotic tail properties of Poisson mixture distributions

Count data are omnipresent in many applied fields, often with overdispersion. With mixtures of Poisson distributions representing an elegant and appealing modelling strategy, we focus here on how the tail behaviour of the mixing distribution is related to the tail of the resulting Poisson mixture. We define five sets of mixing distributions and we identify for each case whenever the Poisson mixture is in, close to or far from a domain of attraction of maxima. We also characterize how the Poisson mixture behaves similarly to a standard Poisson distribution when the mixing distribution has a finite support. Finally, we study, both analytically and numerically, how goodness-of-fit can be assessed with the inspection of tail behaviour.

math.ST↗

arXiv2022

Choice of mixture Poisson models based on Extreme value theory

Count data are omnipresent in many applied fields, often with overdispersion due to an excess of zeroes or extreme values. With mixtures of Poisson distributions representing an elegant and appealing modelling strategy, we focus here on the challenging problem of identifying a suitable mixing distribution and study how extreme value theory can be used. We propose an original strategy to select the most appropriate candidate among three categories: Fr{é}chet, Gumbel and pseudo-Gumbel. Such an approach is presented with the aid of a decision tree and evaluated with numerical simulations.

math.ST↗

arXiv2018

Extension de la régression linéaire généralisée sur composantes supervisées (SCGLR) aux données groupées

We address component-based regularisation of a multivariate Generalized Linear Mixed Model. A set of random responses Y is modelled by a GLMM, using a set X of explanatory variables and a set T of additional covariates. Variables in X are assumed many and redundant: generalized linear mixed regression demands regularisation with respect to X. By contrast, variables in T are assumed few and selected so as to demand no regularisation. Regularisation is performed building an appropriate number of orthogonal components that both contribute to model Y and capture relevant structural information in X. We propose to optimize a SCGLR-specific criterion within a Schall's algorithm in order to estimate the model. This extension of SCGLR is tested on simulated and real data, and compared to Ridge-and Lasso-based regularisations.

stat.ME↗