  Statistical estimation of the prediction uncertainty of physical models is
typically hindered by the inadequacy of these models due to various
approximations they are built upon. The prediction errors due to model
inadequacy can be handled either by correcting the model's results, or by
adapting the model's parameters uncertainty to generate prediction uncertainty
representative, in a way to be defined, of model inadequacy errors. The main
advantage of the latter approach is its transferability to the prediction of
other quantities of interest based on the same parameters. A critical review of
state-of-the-art implementations of this approach in computational chemistry
shows that it is biased, in the sense that it does not produce prediction
uncertainty bands conforming with model inadequacy errors.
