Geostatistical analysis in Bayes spaces: probability densities and compositional data

The focus of this chapter is on spatial statistical methods for functional compositions (FCs). The latter constitutes the generalization to the functional setting of multivariate compositional data. Instances of these data are probability density functions. Our work is fully consistent with the observation that data analyses in a modern geostatistical framework could require resorting to a geometry which is not necessarily the one of the space of square-integrable functions (i.e. L2), depending on the nature of the data. We illustrate the geostatistical framework for FCs, with reference to spatial prediction (kriging) and uncertainty quantification. We exemplify their application in a field scenario where we consider particle-size distributions sampled in a heterogeneous aquifer system.