Multinomial distributions for the parametric modeling of multivariate count data

Pierre Fernique 1, 2 Jean Peyhardi 3, 4, 1 Jean-Baptiste Durand 5
1 VIRTUAL PLANTS - Modeling plant morphogenesis at different scales, from genes to phenotype
CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique, Centre de coopération internationale en recherche agronomique pour le développement [CIRAD] : UMR51
5 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : Two cases of multinomial distributions can be considered: the singular -- for modeling univariate categorical data -- and the non-singular -- for modeling multivariate count data. Considering this latter case, we introduce sum-compound multinomial distributions that encompass re-parameterization of non-singular multinomial and negative multinomial distributions. These compound distributions also enable to generalize univariate distributions and their maximum likelihood estimators to the multivariate case. These distributions are used to address the inference of discrete-state models for tree-structured data. In particular, they allow to introduce parametric multi-type branching processes that can be easily interpreted and efficiently estimated on the basis of data of limited size. The proposed modeling approach is illustrated using plant architecture data sets.
Type de document :
Pré-publication, Document de travail
2016
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https://hal.inria.fr/hal-01286171
Contributeur : Pierre Fernique <>
Soumis le : jeudi 10 mars 2016 - 13:55:57
Dernière modification le : mardi 17 avril 2018 - 09:08:55

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  • HAL Id : hal-01286171, version 1

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Pierre Fernique, Jean Peyhardi, Jean-Baptiste Durand. Multinomial distributions for the parametric modeling of multivariate count data. 2016. 〈hal-01286171〉

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