Estimation of uncertainties from missing higher orders in perturbative calculations

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.

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