  We discuss the statistical properties of parton distributions within the
framework of the NNPDF methodology. We present various tests of statistical
consistency, in particular that the distribution of results does not depend on
the underlying parametrization and that it behaves according to Bayes' theorem
upon the addition of new data. We then study the dependence of results on
consistent or inconsistent datasets and present tools to assess the consistency
of new data. Finally we estimate the relative size of the PDF uncertainty due
to data uncertainties, and that due to the need to infer a functional form from
a finite set of data.
