Object Oriented Geostatistical Simulation of Functional Compositions via Dimensionality Reduction in Bayes spaces

We address the problem of geostatistical simulation of spatial complex data, with emphasis on functional compositions (FCs). We pursue an object oriented geostatistical approach and interpret FCs as random points in a Bayes Hilbert space. This enables us to deal with data dimensionality and constraints by relying on a solid geometric basis, and to develop a simulation strategy consisting of: (i) optimal dimensionality reduction of the problem through a simplicial principal component analysis, and (ii) geostatistical simulation of random realizations of FCs via an approximate multivariate problem.We illustrate our methodology on a dataset of natural soil particle-size densities collected in an alluvial aquifer.