  Using CaWO$_4$ crystals as cryogenic calorimeters, the CRESST experiment
searches for nuclear recoils caused by the scattering of potential Dark Matter
particles. A reliable identification of a potential signal crucially depends on
an accurate background model. In this work we introduce an improved
normalisation method for CRESST's model of the electromagnetic backgrounds.
Spectral templates, based on Geant4 simulations, are normalised via a Bayesian
likelihood fit to experimental background data. Contrary to our previous work,
no assumption of partial secular equilibrium is required, which results in a
more robust and versatile applicability. Furthermore, considering the
correlation between all background components allows us to explain 82.7% of the
experimental background within [1 keV, 40 keV], an improvement of 18.6%
compared to our previous method.
