  The practice of uncertainty quantification (UQ) validation, notably in
machine learning for the physico-chemical sciences, rests on several graphical
methods (scattering plots, calibration curves, reliability diagrams and
confidence curves) which explore complementary aspects of calibration, without
covering all the desirable ones. For instance, none of these methods deals with
the reliability of UQ metrics across the range of input features (adaptivity).
Based on the complementary concepts of consistency and adaptivity, the toolbox
of common validation methods for variance- and intervals- based UQ metrics is
revisited with the aim to provide a better grasp on their capabilities. This
study is conceived as an introduction to UQ validation, and all methods are
derived from a few basic rules. The methods are illustrated and tested on
synthetic datasets and representative examples extracted from the recent
physico-chemical machine learning UQ literature.
