We have periodically (25ms on - 25ms off) illuminated lysozyme crystals with 0.4 THz radiation and simultaneously monitored their X-ray diffraction intensity in order to study non-thermal structural changes in the protein. In this work we analyze the X-ray scaled and unmerged diffraction intensity observations using a multivariate Bayesian model in order to improve the accuracy of the intensity estimates. The diffraction intensity pairs of the illuminated and non-illuminated state show a predominantly positive correlation. The correlation decreases with increasing resolution suggesting that finer slicing and faster sampling of the rocking curve may further improve the accuracy and effect size of structure factor amplitude differences, making the interpretation of structural changes more straightforward. The improved analysis retains the most important structural features described previously (in helix 3) and provide addition details about the B-factor changes close to the substrate binding site.