A probability measure in the space of spectral functions and structure functions

We present a novel technique to parametrize experimental data, based on the construction of a probability measure in the space of functions, which retains the full experimental information on errors and correlations. This measure is constructed in a two step process: first, a Monte Carlo sample of replicas of the experimental data is generated, and then an ensemble of neural network is trained over them. This parametrization does not introduce any bias due to the choice of a fixed functional form. Two applications of this technique are presented. First a probability measure in the space of the spectral function $\rho_{V-A}(s)$ is generated, which incorporates theoretical constraints as chiral sum rules, and is used to evaluate the vacuum condensates. Then we construct a probability measure in the space of the proton structure function $F_2^p(x,Q^2)$, which updates previous work, incorporating HERA data.