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Universitat de Girona. Departament dâ€™InformÃ tica i MatemÃ tica Aplicada  
Egozcue, Juan JosÃ©
PawlowskyGlahn, Vera 

Bayes theorem (discrete case) is taken as a paradigm of information acquisition. As mentionedby Aitchison, Bayes formula can be identified with perturbation of a prior probability vectorand a discrete likelihood function, both vectors being compositional. Considering prior, posteriorand likelihood as elements of the simplex, a natural choice of distance between them is theAitchison distance. Other geometrical features can also be considered using the Aitchison geometry.For instance, orthogonality in the simplex allows to think of orthogonal information, or theperturbationdifference to think of opposite information. The Aitchison norm provides a size ofcompositional vectors, and is thus a natural scalar measure of the information conveyed by thelikelihood or captured by a prior or a posterior. It is called evidence information, or einformationfor short.In order to support such einformation theory some principles of einformation are discussed.They essentially coincide with those of compositional data analysis. Also, a comparison of theseprinciples of einformation with the axiomatic Shannoninformation theory is performed. Shannoninformationand developments thereof do not satisfy scale invariance and also violate subcompositionalcoherence. In general, Shannoninformation theory follows the philosophy of amalgamationwhen relating information given by an evidencevector and some subvector, while the dimensionreduction for the proposed einformation corresponds to orthogonal projections in the simplex. Theresult of this preliminary study is a set of properties of einformation that may constitute the basisof an axiomatic theory. A synthetic example is used to motivate the ideas and the subsequentdiscussion  
http://hdl.handle.net/2072/273653  
eng  
Universitat de Girona. Departament dâ€™InformÃ tica i MatemÃ tica Aplicada  
Tots els drets reservats  
EstadÃstica matemÃ tica  Congressos
Mathematical statistics  Congresses AnÃ lisi multivariable  Congressos Multivariate analysis  Congresses EstadÃstica bayesiana  Congressos Bayesian statistical decision theory  Congresses 

Evidence Information in Bayesian Updating  
info:eurepo/semantics/conferenceObject  
Recercat 