Bayesian analysis of the evidence for minor components in crystallographic models: an alternative to the Hamilton test

A simple test based on Bayesian statistics for the presence of minority populations in single-crystal structure refinement is presented. The test is illustrated by analysis of photocrystallographic experiments on single crystals of ruthenium-sulfur-dioxide-based complexes. In data sets collected after irradiation with light, conventional refinements of the populations of different metastable states to values below 4% are shown to be statistically significant. The results also confirm that the photo-induced states are absent from data collected in the dark.