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Bayesian tools for zero counts in compositional data

The log-ratio methodology makes available powerful tools for analyzing compositional data. Nevertheless, the use of this methodology is only possible for those data sets without null values. Consequently, in those data sets where the zeros are present, a previous treatment becomes necessary. Last advances in the treatment of compositional zeros have been centered especially in the zeros of structural nature and in the rounded zeros. These tools do not contemplate the particular case of count compositional data sets with null values. In this work we deal with \count zeros" and we introduce a treatment based on a mixed Bayesian-multiplicative estimation. We use the Dirichlet probability distribution as a prior and we estimate the posterior probabilities. Then we apply a multiplicative modi¯cation for the non-zero values. We present a case study where this new methodology is applied. Key words: count data, multiplicative replacement, composition, log-ratio analysis

Geologische Vereinigung; Institut d’Estadística de Catalunya; International Association for Mathematical Geology; Càtedra Lluís Santaló d’Aplicacions de la Matemàtica; Generalitat de Catalunya, Departament d’Innovació, Universitats i Recerca; Ministerio de Educación y Ciencia; Ingenio 2010.

Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada

Manager: Daunis i Estadella, Josep
Martín Fernández, Josep Antoni
Other contributions: Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Author: Daunis i Estadella, Josep
Martín Fernández, Josep Antoni
Palarea Albaladejo, Javier
Date: 2008 May 27
Abstract: The log-ratio methodology makes available powerful tools for analyzing compositional data. Nevertheless, the use of this methodology is only possible for those data sets without null values. Consequently, in those data sets where the zeros are present, a previous treatment becomes necessary. Last advances in the treatment of compositional zeros have been centered especially in the zeros of structural nature and in the rounded zeros. These tools do not contemplate the particular case of count compositional data sets with null values. In this work we deal with \count zeros" and we introduce a treatment based on a mixed Bayesian-multiplicative estimation. We use the Dirichlet probability distribution as a prior and we estimate the posterior probabilities. Then we apply a multiplicative modi¯cation for the non-zero values. We present a case study where this new methodology is applied. Key words: count data, multiplicative replacement, composition, log-ratio analysis
Geologische Vereinigung; Institut d’Estadística de Catalunya; International Association for Mathematical Geology; Càtedra Lluís Santaló d’Aplicacions de la Matemàtica; Generalitat de Catalunya, Departament d’Innovació, Universitats i Recerca; Ministerio de Educación y Ciencia; Ingenio 2010.
Format: application/pdf
Citation: Daunis i Estadella, J.; Martín Fernández, J.A.; Palarea Albaladejo, J. ’Bayesian tools for zero counts in compositional data’ a CODAWORK’08. Girona: La Universitat, 2008 [consulta: 12 maig 2008]. Necessita Adobe Acrobat. Disponible a Internet a: http://hdl.handle.net/10256/713
Document access: http://hdl.handle.net/10256/713
Language: eng
Publisher: Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Rights: Tots els drets reservats
Subject: Estadística bayesiana
Dirichlet, Sèries de
Title: Bayesian tools for zero counts in compositional data
Type: info:eu-repo/semantics/conferenceObject
Repository: DUGiDocs

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