Splitting models for multivariate count data

Jean Peyhardi (1) , Pierre Fernique (2) , Jean-Baptiste Durand (3)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 UMR AGAP - Amélioration génétique et adaptation des plantes méditerranéennes et tropicales
3 STATIFY - Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension

We investigate the class of splitting distributions as the composition of a singular multivariate distribution and a univariate distribution. It will be shown that most common parametric count distributions (multinomial, negative multinomial, multivariate hypergeometric, multivariate negative hypergeometric, …) can be written as splitting distributions with separate parameters for both components, thus facilitating their interpretation, inference, the study of their probabilistic characteristics and their extensions to regression models. We highlight many probabilistic properties deriving from the compound aspect of splitting distributions and their underlying algebraic properties. Parameter inference and model selection are thus reduced to two separate problems, preserving time and space complexity of the base models. Based on this principle, we introduce several new distributions. In the case of multinomial splitting distributions, conditional independence and asymptotic normality properties for estimators are obtained. Mixtures of splitting regression models are used on a mango tree dataset in order to analyze the patchiness.

Mots clés: Compound distribution; Multivariate extension; Probabilistic graphical model; Singular multivariate distribution; compound distribution; singular multivariate distribution; multivariate extension; probabilistic graphical model

Domaines: Statistiques [math.ST]

Jean Peyhardi, Pierre Fernique, Jean-Baptiste Durand. Splitting models for multivariate count data. Journal of Multivariate Analysis, 2021, 181, pp.104677. ⟨10.1016/j.jmva.2020.104677⟩. ⟨hal-02962877⟩