We provide novel probabilistic portrayals of two multivariate models designed to handle zero-inflation in count-compositional data. We develop a new unifying framework that represents both as finite mixture distributions. One of these distributions, based on Dirichlet-multinomial components, has been studied before, but has not yet been properly characterised as a sampling distribution of the counts. The other, based on multinomial components, is a new contribution. Using our finite mixture representations enables us to derive key statistical properties, including moments, marginal distributions, and special cases for both distributions. We develop enhanced Bayesian inference schemes with efficient Gibbs sampling updates, wherever possible, for parameters and auxiliary variables, demonstrating improvements over existing methods in the literature. We conduct simulation studies to evaluate the efficiency of the Bayesian inference procedures and to illustrate the practical utility of the proposed distributions.

翻译：本文为两种旨在处理计数组合数据中零膨胀问题的多元模型提供了新颖的概率刻画。我们建立了一个新的统一框架，将这两种模型表示为有限混合分布。其中一种基于狄利克雷-多项分量的分布虽已有研究，但尚未被恰当地表征为计数的抽样分布。另一种基于多项分量的分布则是本文的新贡献。通过有限混合表示，我们推导出两种分布的关键统计性质，包括矩、边缘分布及特殊情形。我们开发了增强的贝叶斯推断方案，在可能的情况下对参数和辅助变量采用高效的吉布斯采样更新，证明了其相对于现有文献方法的改进。通过模拟研究，我们评估了贝叶斯推断程序的效率，并展示了所提出分布的实际效用。