Vera Pawlowski-Glahn and Ricardo A. Olea: Geostatistical analysis of compositional data
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Vera Pawlowski-Glahn and Ricardo A. Olea: Geostatistical analysis of compositional data Oxford University Press, Oxford, 2004 Helmut Schaeben
Published online: 8 August 2007 © International Association for Mathematical Geology 2007
Both authors of the above book are well known in the mathematical geology community for their contributions to the analysis of compositional data (VP-G) and geostatistics (RAO). The book is a joint effort to bring the two issues together; the subject of the book originates in VP-G’s PhD thesis at the Free University of Berlin back in 1986. Twenty years later, this IAMG monograph is still the first and only book to address these issues even though substantial progress in the understanding of compositional data analysis has been accomplished in that period, not least thanks to the first author herself, her coworkers, and others as documented by the series of workshops on compositional data analysis in Girona, Spain, over the last years. The peculiar problem with compositional data is that the conventional correlation to measure linear dependence does not apply. Usually compositions are immediately associated with multivariate data, and therefore the proper approach taken by the authors is coregionalization and cokriging. Nevertheless, even in the univariate case of concentration data measured in ppm, the negligence of their finite domain generally leads to useless results (e.g. Goovaerts 1997; p. 261), prohibitive of any reasonable interpretation. Thus, the scope of the book is to develop a concept of generalized spatial correlation for data for which already the notion of common correlation does not apply. The book follows the usual steps from classical statistics to “classical” geostatistics by way of generalization of random variables to random functions and from moments to functions defined in the spatial domain, with its major achievements, the definition of the variogram and the covariance function for the multivariate case, and a methodology to construct proper approximations of them based on data. H. Schaeben () Mathematische Geologie und Geoinformatik, Institut für Geologie, TU Bergakademie Freiberg, Bernhard-von-Cotta Str. 2, 09596 Freiberg, Germany e-mail: [email protected]
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Math Geol (2007) 39: 435–437
Each chapter commences with a non-technical introduction gently exposing the general ideas to be elaborated on. These introductions largely facilitate the readability, as the notation itself requires some patience by the reader before she or he becomes acquainted with it. The book is very well organized and written in a very instructive way. However, to appreciate the presentation, the reader should have some knowledge in compositional data analysis as developed by John Aitchison (Aitchison 1982, 1986) and made available again in 2003 (Aitchison 2003). The chapter entitled Regionalized Compositions adapts the notions of compositions and random functions to each other. The additive and the centered logratio transformations are introduced. Sufficient as well as ne
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