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With current high precision collider data, the reliable estimation oftheoretical uncertainties due to missing higher orders (MHOs) in perturbationtheory has become a pressing issue for collider phenomenology. Traditionally,the size of the MHOs is estimated through scale variation, a simple but ad hocmethod without probabilistic interpretation. Bayesian approaches provide acompelling alternative to estimate the size of the MHOs, but it is not clearhow to interpret the perturbative scales, like the factorisation andrenormalisation scales, in a Bayesian framework. Recently, it was proposed thatthe scales can be incorporated as hidden parameters into a Bayesian model. Inthis paper, we thoroughly scrutinise Bayesian approaches to MHO estimation andsystematically study the performance of different models on an extensive set ofhigh-order calculations. We extend the framework in two significant ways.First, we define a new model that allows for asymmetric probabilitydistributions. Second, we introduce a prescription to incorporate informationon perturbative scales without interpreting them as hidden model parameters. Weclarify how the two scale prescriptions bias the result towards specific scalechoice, and we discuss and compare different Bayesian MHO estimates amongthemselves and to the traditional scale variation approach. Finally, we providea practical prescription of how existing perturbative results at the standardscale variation points can be converted to 68%/95% credibility intervals in theBayesian approach using the new public code MiHO.

An analysis of Bayesian estimates for missing higher orders in perturbative calculations