Zemach moments of the proton from Bayesian inference

The first and the third Zemach moments are obtained, < r >((2)) = 1.1108 +/- 0.0021 fm and < r(3)>((2)) = 2.889 +/- 0.008 fm(3), from the Bayesian analysis of the elastic ep scattering data. The quantitative discussion of the dependence of the results on the parametrization choice is presented and the corresponding systematic uncertainties are estimated-about 0.6% and 1.6% for the first and the third Zemach moments, respectively.