2008/09/17 by Adam Butler, Chris Glasbey, C. A. Glasbey · 1 citation
Computer Science · Engineering · Environmental Science · #Geochemistry and Geologic Mapping #Mineral Processing and Grinding #Soil Geostatistics and Mapping
paper · doi:10.1111/j.1467-9876.2008.00627.x
crossref issued 2008/09/17 · crossref published 2008/09/17 · crossref published-online 2008/09/17 · openalex publication_date 2008/09/17 · crossref created 2008/09/17 · crossref published-print 2008/12/01 · crossref deposited 2025/01/31 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/30
Summary Compositional data record the relative proportions of different components within a mixture and arise frequently in many fields. Standard statistical techniques for the analysis of such data assume the absence of proportions which are genuinely zero. However, real data can contain a substantial number of zero values. We present a latent Gaussian model for the analysis of compositional data which contain zero values, which is based on assuming that the data arise from a (deterministic) Euclidean projection of a multivariate Gaussian random variable onto the unit simplex. We propose an iterative algorithm to simulate values from this model and apply the model to data on the proportions of fat, protein and carbohydrate in different groups of food products. Finally, evaluation of the likelihood involves the calculation of difficult integrals if the number of components is more than 3, so we present a hybrid Gibbs rejection sampling scheme that can be used to draw inferences about the parameters of the model when the number of components is arbitrarily large.