Parton distributions: determining probabilities in a space of functions

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.