The empirical Bayes approach
As detailed in Chapter 2, in addition to the likelihood, Bayesian analysis depends on a prior distribution for the model parameters. This prior can be nonparametric or parametric, depending on unknown parameters that may in turn be drawn from some second-stage prior. This sequence of parameters and priors constitutes a hierarchical model. The hierarchy must stop at some point, with all remaining prior parameters assumed known. Rather than make this assumption, the empirical Bayes (EB) approach uses the observed data to estimate these ﬁnal stage parameters (or to directly estimate the Bayes decision rule) and then proceeds as though the prior were known.