  In this proceeding we present the results of our recent study
(hep-ph/1409.5036) of the statistical performances of two different approaches,
Scale Variation (SV) and the Bayesian model of Cacciari and Houdeau
(CH)(hep-ph/1105.5152) (which we also extend to observables with initial state
hadrons), to the estimation of Missing Higher-Order Uncertainties
(MHOUs)(hep-ph/1307.1843) in perturbation theory. The behavior of the models is
determined by analyzing, on a wide set of observables, how the MHOU intervals
they produce are successful in predicting the next orders. We observe that the
Bayesian model behaves consistently, producing intervals at $68\%$ Degree of
Belief (DoB) comparable with the scale variation intervals with a rescaling
factor $r$ larger than $2$ and closer to $4$. Concerning SV, our analysis
allows the derivation of a heuristic Confidence Level (CL) for the intervals.
We find that assigning a CL of $68\%$ to the intervals obtained with the
conventional choice of varying the scales within a factor of two with respect
to the central scale could potentially lead to an underestimation of the
uncertainties in the case of observables with initial state hadrons.
