Estimation of uncertainties from missing higher orders in perturbative calculations

TL;DR

This paper compares two methods, Scale Variation and Bayesian modeling, for estimating uncertainties in perturbative calculations, finding Bayesian methods provide more consistent and reliable uncertainty intervals.

Contribution

The study extends Bayesian models to observables with initial state hadrons and evaluates their performance against traditional scale variation methods.

Findings

Bayesian model produces consistent 68% DoB intervals with rescaling factors between 2 and 4.

Scale variation may underestimate uncertainties for observables with initial state hadrons.

Bayesian approach offers a more reliable estimation of missing higher-order uncertainties.

Abstract

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.