Hierarchical Regression

There isn’t a single authorative definition of a hierarchical model. Gelman et al. (1995) discuss two definitions: 1. “Estimating the population distribution of unonobserved parameters” 2. “Multiple parameters related by the structure of the problem” Intuitively, knowing something about one “experiment” tells us something about another. For example: Multiple similar experiments Similar measurements from different locations Several tasks to perform on the same set of images We’ve seen the last case when we talked about mixed-membership models. These are one type of hierarchical model. When talking about hierarchical models, statiticians sometimes use the phrase “sharing statistical strength.” The idea is that something we can infer well in one group of data can help us with something we cannot infer well in another. For example, we may have a lot of data from California but much less data from Oregon. What we learn from California should help us learn in Oregon. The key idea is: Inference about one unobserved quantity affects inference about another unobserved quantity.