3.4 Shrinkage
To show you one of the main consequences of hierarchical models, I will require your assistance, so please join me in a brief experiment. I will need you to print and save the summary computed with az.summary(idata_h). Then, I want you to rerun the model two more times after making small changes to the synthetic data. Remember to save the summary after each run. In total, we will have three runs:
One run setting all the elements of
G_samplesto 18One run setting all the elements of
G_samplesto 3One last run setting one element to 18 and the other two to 3
Before continuing, please take a moment to think about the outcome of this experiment. Focus on the estimated mean value of θ in each experiment. Based on the first two runs of the model, could you predict the outcome for the third case?
If we put the result in a table, we get something more or less like this; remember that small variations could occur due to the stochastic nature of the sampling process:
