  Statistical learning algorithms provide a generally-applicable framework to
sidestep time-consuming experiments, or accurate physics-based modeling, but
they introduce a further source of error on top of the intrinsic limitations of
the experimental or theoretical setup. Uncertainty estimation is essential to
quantify this error, and make application of data-centric approaches more
trustworthy. To ensure that uncertainty quantification is used widely, one
should aim for algorithms that are reasonably accurate, but also easy to
implement and apply. In particular, including uncertainty quantification on top
of an existing architecture should be straightforward, and add minimal
computational overhead. Furthermore, it should be easy to manipulate or combine
multiple machine-learning predictions, propagating uncertainty over further
modeling steps. We compare several well-established uncertainty quantification
frameworks against these requirements, and propose a practical approach, which
we dub direct propagation of shallow ensembles, that provides a good compromise
between ease of use and accuracy. We present benchmarks for generic datasets,
and an in-depth study of applications to the field of atomistic machine
learning for chemistry and materials. These examples underscore the importance
of using a formulation that allows propagating errors without making strong
assumptions on the correlations between different predictions of the model.
