Finite mixture representations of zero-and-$N$-inflated distributions for count-compositional data
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910082665545728 |
|---|---|
| author | Menezes, André F. B. Parnell, Andrew C. Murphy, Keefe |
| author_facet | Menezes, André F. B. Parnell, Andrew C. Murphy, Keefe |
| contents | 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 present applications to a human gut microbiome dataset to illustrate the practical utility of the proposed distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13879 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite mixture representations of zero-and-$N$-inflated distributions for count-compositional data Menezes, André F. B. Parnell, Andrew C. Murphy, Keefe Methodology Statistics Theory 62H05, 62F15, 62H30 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 present applications to a human gut microbiome dataset to illustrate the practical utility of the proposed distributions. |
| title | Finite mixture representations of zero-and-$N$-inflated distributions for count-compositional data |
| topic | Methodology Statistics Theory 62H05, 62F15, 62H30 |
| url | https://arxiv.org/abs/2501.13879 |