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 improve significantly the accuracy of the original approach. I will further show how scale dependence can be "removed" from a perturbative result within the context of these models.