  The choice of data that enters a global QCD analysis can have a substantial
impact on the resulting parton distributions and their predictions for collider
observables. One of the main reasons for this has to do with the possible
presence of inconsistencies, either internal within an experiment or external
between different experiments. In order to assess the robustness of the global
fit, different definitions of a conservative PDF set, that is, a PDF set based
on a maximally consistent dataset, have been introduced. However, these
approaches are typically affected by theory biases in the selection of the
dataset. In this contribution, after a brief overview of recent NNPDF
developments, we propose a new, fully objective, definition of a conservative
PDF set, based on the Bayesian reweighting approach. Using the new NNPDF3.0
framework, we produce various conservative sets, which turn out to be mutually
in agreement within the respective PDF uncertainties, as well as with the
global fit. We explore some of their implications for LHC phenomenology,
finding also good consistency with the global fit result. These results provide
a non-trivial validation test of the new NNPDF3.0 fitting methodology, and
indicate that possible inconsistencies in the fitted dataset do not affect
substantially the global fit PDFs.
