The Bayesian approach for the feed-forward neural networks is reviewed. Its potential for usage in hadron physics is discussed. As an example of the application the study of the the two-photon exchange effect is presented. We focus on the model comparison, the estimation of the systematic uncertainties due to the choice of the model, and the over-fitting. As an illustration the predictions of the cross sections ratio dσ(e + p → e + p)/dσ(e − p → e − p) are given together with the estimate of the uncertainty due to the parametrization choice.