3.5 Hierarchies all the way up

Various data structures lend themselves to hierarchical descriptions that can encompass multiple levels. For example, consider professional football (soccer) players. As in many other sports, players have different positions. We may be interested in estimating some skill metrics for each player, for the positions, and for the overall group of professional football players. This kind of hierarchical structure can be found in many other domains as well:

• Medical research: Suppose we are interested in estimating the effectiveness of different drugs for treating a particular disease. We can categorize patients based on their demographic information, disease severity, and other relevant factors and build a hierarchical model to estimate the probability of cure or treatment success for each subgroup. We can then use the parameters of the subgroup distribution to estimate the overall probability of cure or treatment success for the entire patient population.

• Environmental...