Proton radius from Bayesian inference

The methods of Bayesian statistics are used to extract the value of the proton radius from the elastic ep scattering data in a model-independent way. To achieve that goal a large number of parametrizations (equivalent to neural network schemes) are considered and ranked by their conditional probability P(parametrization vertical bar data) instead of using the minimal error criterion. As a result the most probable proton radii values (r(E)(p) = 0.899 +/- 0.003 fm, r(M)(p) = 0.879 +/- 0.007 fm) are obtained and systematic error due to freedom in the choice of parametrization is estimated. Correcting the data for the two-photon-exchange effect leads to smaller differences between the extracted values of r(E)(p) and r(M)(p). The results disagree with recent muonic atom measurements.