Hierarchical bayes (multi-level model)¶
A key requirement for computing the posterior \(p(\theta| D)\)is the specification of a prior \(p(\theta| \eta)\), where \(\eta\) is a hyper-parameter. (The bayesian way is to put priors on top of priors) In Hierarchical bayes we assume that this hyper parameter is unknown, and we model our uncertainity by putting a prior on top of this hyper parameter (Hyper prior).
We can use hierarchical modeling to enable data sharing, where we can borrow statistical strength from data rich observations.