We construct a parametrization of deep-inelastic structure functions which
retains information on experimental errors and correlations, and which does not
introduce any theoretical bias while interpolating between existing data
points. We generate a Monte Carlo sample of pseudo-data configurations and we
train an ensemble of neural networks on them. This effectively provides us with
a probability measure in the space of structure functions, within the whole
kinematic region where data are available. This measure can then be used to
determine the value of the structure function, its error, point-to-point
correlations and generally the value and uncertainty of any function of the
structure function itself. We apply this technique to the determination of the
structure function F_2 of the proton and deuteron, and a precision
determination of the isotriplet combination F_2[p-d]. We discuss in detail
these results, check their stability and accuracy, and make them available in
various formats for applications.Comment: Latex, 43 pages, 22 figures. (v2) Final version, published in JHEP;
Sect.5.2 and Fig.9 improved, a few typos corrected and other minor
improvements. (v3) Some inconsequential typos in Tab.1 and Tab 5 corrected.
Neural parametrization available at http://sophia.ecm.ub.es/f2neura