  We report on an analysis of the impact of available experimental data on hard
processes in proton-lead collisions during Run I at the Large Hadron Collider
on nuclear modifications of parton distribution functions. Our analysis is
restricted to the EPS09 and DSSZ global fits. The measurements that we consider
comprise production of massive gauge bosons, jets, charged hadrons and pions.
This is the first time a study of nuclear PDFs includes this number of
different observables. The goal of the paper is twofold: i) checking the
description of the data by nPDFs, as well as the relevance of these nuclear
effects, in a quantitative manner; ii) testing the constraining power of these
data in eventual global fits, for which we use the Bayesian reweighting
technique. We find an overall good, even too good, description of the data,
indicating that more constraining power would require a better control over the
systematic uncertainties and/or the proper proton-proton reference from LHC Run
II. Some of the observables, however, show sizable tension with specific
choices of proton and nuclear PDFs. We also comment on the corresponding
improvements on the theoretical treatment.
