The influence of the error-propagation on ilr-base selection for compositional models

Most data in the geoenvironmental sciences are compositional. If this data is not treated adequately, the results obtained from its numerical
modelling could be wrong. The log-ratio transformation was proposed to resolve the principal statistical problems related to compositional data
(CoDa). The isometric-log-ratio transformation (ilr) is the most used due to its advantage to represent the simplex space orthogonally. For this
purpose, it is required to define an orthonormal base, and one method is through the Sequential Binary Partition (SBP) that is an iterative process.
However, recent modelling researches with a compositional approach applied to energy and air pollution has found that different select order in the
SBP produces different results. This behaviour from the practical numerical modelling could contradict the theory of CoDa. The aim is to explain
the problem through an error-propagation approach. It is necessary to consider the finite arithmetic implicated in the numeric modelling software.
The results are exposed using air pollution data.