  Bayesian Model Calibration is used to revisit the problem of scaling factor
calibration for semi-empirical correction of ab initio harmonic properties
(e.g. vibrational frequencies and zero-point energies). A particular attention
is devoted to the evaluation of scaling factor uncertainty, and to its effect
on the accuracy of scaled properties. We argue that in most cases of interest
the standard calibration model is not statistically valid, in the sense that it
is not able to fit experimental calibration data within their uncertainty
limits. This impairs any attempt to use the results of the standard model for
uncertainty analysis and/or uncertainty propagation. We propose to include a
stochastic term in the calibration model to account for model inadequacy. This
new model is validated in the Bayesian Model Calibration framework. We provide
explicit formulae for prediction uncertainty in typical limit cases: large and
small calibration sets of data with negligible measurement uncertainty, and
datasets with large measurement uncertainties.
