To verify that we have implemented our hierarchical Bayes algorithms correctly we briefly describe the results of using synthetic data to test our inference procedure. Figure shows the sampled distributions of the hyper-parameters. The dashed lines indicate the expected peak of each distribution, as calculated from the sample mean and variance of the ten true values of θ true . As can be seen the hierarchical MCMC algorithm obtains the correct peak for all the five different mean and variance hyper-parameters.