  The parton distribution functions (PDFs) which characterize the structure of
the proton are currently one of the dominant sources of uncertainty in the
predictions for most processes measured at the Large Hadron Collider (LHC).
Here we present the first extraction of the proton PDFs that accounts for the
missing higher order uncertainty (MHOU) in the fixed-order QCD calculations
used in PDF determinations. We demonstrate that the MHOU can be included as a
contribution to the covariance matrix used for the PDF fit, and then introduce
prescriptions for the computation of this covariance matrix using scale
variations. We validate our results at next-to-leading order (NLO) by
comparison to the known next order (NNLO) corrections. We then construct
variants of the NNPDF3.1 NLO PDF set that include the effect of the MHOU, and
assess their impact on the central values and uncertainties of the resulting
PDFs.
