The chief benefit of the hierarchical model is that it allows us to quantify (with the hyper-parameters) the variability of the parameters between different experiments. Figure shows the histograms for the hyper-parameters samples of µ (left) and Σ (right). Also shown as vertical dashed lines are the the sample mean and variance of the concatenated ten θ i chains. The most obvious feature of these plots is that these hyper-parameter distributions clearly show a much wider confidence interval as compared with the individual θ i distributions. While the value of each parameter for each individual experiment is known with high accuracy, once the variability between experiments is taken into account we see that the possible parameter range is significantly broadened.