3.7 Exercises

1. Using your own words explain the following concepts in two or three sentences:

   • Complete pooling

   • No pooling

   • Partial pooling

2. Repeat the exercise we did with model_h. This time, without a hierarchical structure, use a flat prior such as Beta(α = 1,β = 1). Compare the results of both models.

3. Create a hierarchical version of the tips example from Chapter 2, by partially pooling across the days of the week. Compare the results to those obtained without the hierarchical structure.

4. For each subpanel in Figure 3.7, add a reference line representing the empirical mean value at each level, that is, the global mean, the forward mean, and Messi’s mean. Compare the empirical values to the posterior mean values. What do you observe?

5. Amino acids are usually grouped into categories such as polar, non-polar, charged, and special. Build a hierarchical model similar to cs_h but including a group effect for the amino acid category. Compare the results to those...