  We present the MCscales approach for incorporating scale uncertainties in
parton distribution functions (PDFs). The new methodology builds on the Monte
Carlo sampling for propagating experimental uncertainties into the PDF space
that underlies the NNPDF approach, but it extends it to the space of
factorisation and renomalisation scales. A prior probability is assigned to
each scale combinations set in the theoretical predictions used to obtain each
PDF replica in the Monte Carlo ensemble and a posterior probability is obtained
by selecting replicas that satisfy fit-quality criteria. Our approach allows
one to exactly match the scale variations in the PDFs with those in the
computation of the partonic cross sections, thus accounting for the full
correlations between the two. We illustrate the opportunities for
phenomenological exploration made possible by our methodology for a variety of
LHC observables. Sets of PDFs enriched with scale information are provided,
along with a set of tools to use them.
