Quantifying rock fabrics: a test of autocorrelation of the spatial distribution of cristals

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dc.contributor Universitat de Girona. Departament d'Informàtica i Matemàtica Aplicada
dc.contributor.author Egozcue, Juan José
dc.contributor.author Mackenzie, J.R.
dc.contributor.author Heilbronner, Renée
dc.contributor.author Hielscher, Ralf
dc.contributor.author Müller, A.
dc.contributor.author Schaeben, Helmut
dc.contributor.editor Daunis i Estadella, Josep
dc.contributor.editor Martín Fernández, Josep Antoni
dc.date.issued 2008-05-28
dc.identifier.citation 'Quantifying rock fabrics: a test of autocorrelation of the spatial distribution of cristals' a CODAWORK’08. Girona: La Universitat, 2008 [consulta: 12 maig 2008]. Necessita Adobe Acrobat. Disponible a Internet a: http://hdl.handle.net/10256/719
dc.identifier.uri http://hdl.handle.net/10256/719
dc.description.abstract A novel test of spatial independence of the distribution of crystals or phases in rocks based on compositional statistics is introduced. It improves and generalizes the common joins-count statistics known from map analysis in geographic information systems. Assigning phases independently to objects in RD is modelled by a single-trial multinomial random function Z(x), where the probabilities of phases add to one and are explicitly modelled as compositions in the K-part simplex SK. Thus, apparent inconsistencies of the tests based on the conventional joins{count statistics and their possibly contradictory interpretations are avoided. In practical applications we assume that the probabilities of phases do not depend on the location but are identical everywhere in the domain of de nition. Thus, the model involves the sum of r independent identical multinomial distributed 1-trial random variables which is an r-trial multinomial distributed random variable. The probabilities of the distribution of the r counts can be considered as a composition in the Q-part simplex SQ. They span the so called Hardy-Weinberg manifold H that is proved to be a K-1-affine subspace of SQ. This is a generalisation of the well-known Hardy-Weinberg law of genetics. If the assignment of phases accounts for some kind of spatial dependence, then the r-trial probabilities do not remain on H. This suggests the use of the Aitchison distance between observed probabilities to H to test dependence. Moreover, when there is a spatial uctuation of the multinomial probabilities, the observed r-trial probabilities move on H. This shift can be used as to check for these uctuations. A practical procedure and an algorithm to perform the test have been developed. Some cases applied to simulated and real data are presented. Key words: Spatial distribution of crystals in rocks, spatial distribution of phases, joins-count statistics, multinomial distribution, Hardy-Weinberg law, Hardy-Weinberg manifold, Aitchison geometry
dc.description.sponsorship 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.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
dc.rights Tots els drets reservats
dc.subject Hardy, Espais de
dc.subject Anàlisi funcional
dc.title Quantifying rock fabrics: a test of autocorrelation of the spatial distribution of cristals
dc.type info:eu-repo/semantics/conferenceObject

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