Show simple item record

dc.contributor.authorOrtego Martínez, María Isabel
dc.contributor.authorEgozcue Rubí, Juan José
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental
dc.identifier.citationOrtego, M.I., Egozcue, J. J. Bayesian estimation of the orthogonal decomposition of a contingency table. "Austrian Journal of Statistics", 2016, vol. 45, núm. 4, p. 45-56.
dc.description.abstractIn a multinomial sampling, contingency tables can be parametrized by probabilities of each cell. These probabilities constitute the joint probability function of two or more discrete random variables. These probability tables have been previously studied from a compositional point of view. The compositional analysis of probability tables ensures coherence when analysing sub-tables. The main results are: (1) given a probability table, the closest independent probability table is the product of their geometric marginals; (2) the probability table can be orthogonally decomposed into an independent table and an interaction table; (3) the departure of independence can be measured using simplicial deviance, which is the Aitchison square norm of the interaction table. In previous works, the analysis has been performed from a frequentist point of view. This contribution is aimed at providing a Bayesian assessment of the decomposition. The resulting model is a log-linear one, which parameters are the centered log-ratio transformations of the geometric marginals and the interaction table. Using a Dirichlet prior distribution of multinomial probabilities, the posterior distribution of multinomial probabilities is again a Dirichlet distribution. Simulation of this posterior allows to study the distribution of marginal and interaction parameters, checking the independence of the observed contingency table and cell interactions. The results corresponding to a two-way contingency table example are presented.
dc.format.extent12 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
dc.subject.lcshSampling (Statistics)
dc.subject.othersimplicial deviance
dc.subject.othermultinomial sampling
dc.subject.otherAitchison geometry of the simplex
dc.subject.otherorthogonal decomposition
dc.titleBayesian estimation of the orthogonal decomposition of a contingency table
dc.subject.lemacMostreig (Estadística)
dc.contributor.groupUniversitat Politècnica de Catalunya. COSDA-UPC - COmpositional and Spatial Data Analysis
dc.description.peerreviewedPeer Reviewed
dc.rights.accessOpen Access
dc.description.versionPostprint (published version)
local.citation.authorOrtego, M.I.; Egozcue, J. J.
local.citation.publicationNameAustrian Journal of Statistics

Files in this item


This item appears in the following Collection(s)

Show simple item record

Attribution 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution 3.0 Spain