Inference of distributional parameters from compositional samples containing nondetects

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Abstract

Low concentrations of elements in geochemical analyses have the peculiarity of being compositional data and, for a given level of significance, are likely to be beyond the capabilities of laboratories to distinguish between minute concentrations and complete absence, thus preventing laboratories from reporting extremely low concentrations of the analyte. Instead, what is reported is the detection limit, which is the minimum concentration that conclusively differentiates between presence and absence of the element. A spatially distributed exhaustive sample is employed in this study to generate unbiased sub-samples, which are further censored to observe the effect that different detection limits and sample sizes have on the inference of population distributions starting from geochemical analyses having specimens below detection limit (nondetects). The isometric logratio transformation is used to convert the compositional data in the simplex to samples in real space, thus allowing the practitioner to properly borrow from the large source of statistical techniques valid only in real space. The bootstrap method is used to numerically investigate the reliability of inferring several distributional parameters employing different forms of imputation for the censored data. The case study illustrates that, in general, best results are obtained when imputations are made using the distribution best fitting the readings above detection limit and exposes the problems of other more widely used practices. When the sample is spatially correlated, it
is necessary to combine the bootstrap with stochastic simulation. 

Additional publication details

Publication type Conference Paper
Publication Subtype Conference Paper
Title Inference of distributional parameters from compositional samples containing nondetects
Year Published 2009
Language English
Publisher Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Contributing office(s) Eastern Energy Resources Science Center
Description 20 p.
Larger Work Type Book
Larger Work Subtype Conference publication
Larger Work Title CODAWORK’08
Conference Title ​ 3rd Compositional Data Analysis Workshop
Conference Location Girona, Spain
Conference Date May 27-30, 2008