Top, Bayesian P values (BpV) for the full model indicating goodness of fit, based on posterior discrepancy. Points are Freeman–Tukey differences between observed and expected values, and simulated and expected values within the MCMC scheme (n = 10,000). Plot shows no evidence for lack of fit between the model and the data. Bottom, Posterior distribution for the degrees of freedom parameter (ν) in our supplementary analysis of candidate distributions. The highest posterior density of 3.46, with 97.5% of the total posterior density below 4 provides strong evidence in favour of a non-central t distribution relative to a normal distribution and supports the use of 3.5 for ν.