Figures 13a and 13b display the results of these analyses with and without hyperparameters. Without hyperparameters, the best fit model lies between **data** sets A and B, which follow the same trend, and set C, which has a different intercept. In contrast, the best fit model using hyperparameters, shown in Fig. 13b agrees with the true model used to generate the **data** in this example. In this figure we have scaled the Likelihood for both models we find a values −2.6 for the model with hyperparameters and −323.2 without.