A new method is introduced for characterising vertical-cavity surface-emitting lasers. This approach relies on the direct application of Bayes' theorem from classical probability theory on time-series data of polarisation measurements. The technique is shown to work for the simplified one-dimensional dynamics of the laser as an overdamped particle in a double-well potential driven by fluctuations, as well as for the most complicated case of fluctuational motion on the Poincaré sphere about one of the linearly-polarised states.