Tree Pólya Splitting distributions for multivariate count data
提出一类新的多元计数分布——树状Pólya分裂分布，它结合单变量分布与沿固定划分树的奇异多元分布，能灵活建模观测层面的正、负或零相关结构，并以毛翅目丰度数据展示其理论性质与拟合优势。
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 offer some flexibility, allowing for the modeling of complex dependence structures (positive, negative, or null) at the observation level. Specifically, we present 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 microbial analysis.