We present the results of a Bayesian analysis of a Regge model to describe the background contribution for K+Λ and K+Σ0 photoproduction. The model is based on the exchange of K+(494) and K*+(892) trajectories in the t-channel. We utilise the Bayesian evidence Z to determine the best model variant for each channel. The Bayesian evidence integrals were calculated using the Nested Sampling algorithm. For different prior widths, we find decisive Bayesian evidence (ΔlnZ≈24) for a K+Λ photoproduction Regge model with a positive vector coupling and a negative tensor coupling constant for the K*+(892) trajectory, and a rotating phase factor for both trajectories. Using the Χ2 minimisation method, one could not draw this conclusion from the same dataset. For the K+Σ0 photoproduction Regge model, on the other hand, the difference between the evidence integrals is insufficient to pinpoint one model variant.