In many branches of physics, and in particular in quantum field theory, the perturbative approach offers a powerful tool for making theoretical predictions. When the expansion parameter is not small enough, as it happens in quantum chromodynamics, and the number of computable orders is limited, it becomes very important to be able to estimate the uncertainty on a theoretical prediction due to the missing higher orders. This is particularly important when comparing theory with data, e.g. for the precision physics programme of the LHC.
I will review the standard method, which is based on unphysical scale variation. While scale variation is certainly a good tool to guess the size of the next perturbative order, it lacks of a probabilistic interpretation and it often underestimates the actual uncertainty. A few years ago Cacciari and Houdeau proposed a Bayesian model to give a statistical meaning to theory uncertainties. I will review the Cacciari-Houdeau approach, and present new models which overcomes some of the limitations of the original one. I will further show how scale dependence can be removed from a finite-order result within the context of these models. As a proof of concept, I will apply the methods to inclusive Higgs production in gluon fusion, for which four perturbative orders are known, and which is characterised by large perturbative corrections.