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 caused by model inadequacy can be handled either by correcting the model’s results or by adapting the model’s parameter uncertainty to generate prediction uncertainties representative, in a way to be defined, of model inadequacy errors. The main advantage of the latter approach (thereafter called PUI, for Parameter Uncertainty Inflation) is its transferability to the prediction of other quantities of interest based on the same parameters. A critical review of implementations of PUI in several areas of computational chemistry shows that it is biased, in the sense that it does not produce prediction uncertainty bands conforming to model inadequacy errors.