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Dirichlet composition distribution for compositional data with zero components: An application to fluorescence in situ hybridization (FISH) detection of chromosome

Zeros in compositional data are very common and can be classified into rounded and essential zeros. The rounded zero refers to a small proportion or below detection limit value, while the essential zero refers to the complete absence of the component in the composition. In this article, we propose a...

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Detalles Bibliográficos
Autores principales: Tang, Man‐Lai, Wu, Qin, Yang, Sheng, Tian, Guo‐Liang
Formato: Online Artículo Texto
Lenguaje:English
Publicado: John Wiley and Sons Inc. 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9300144/
https://www.ncbi.nlm.nih.gov/pubmed/34914842
http://dx.doi.org/10.1002/bimj.202000334
Descripción
Sumario:Zeros in compositional data are very common and can be classified into rounded and essential zeros. The rounded zero refers to a small proportion or below detection limit value, while the essential zero refers to the complete absence of the component in the composition. In this article, we propose a new framework for analyzing compositional data with zero entries by introducing a stochastic representation. In particular, a new distribution, namely the Dirichlet composition distribution, is developed to accommodate the possible essential‐zero feature in compositional data. We derive its distributional properties (e.g., its moments). The calculation of maximum likelihood estimates via the Expectation‐Maximization (EM) algorithm will be proposed. The regression model based on the new Dirichlet composition distribution will be considered. Simulation studies are conducted to evaluate the performance of the proposed methodologies. Finally, our method is employed to analyze a dataset of fluorescence in situ hybridization (FISH) for chromosome detection.