Intelligent smoothing using hierarchical Bayesian models

Hierarchical Bayesian modeling provides a flexible approach to modeling in multiparameter problems. Examples include disease mapping and spatiotemporal analysis, and multiple exposure modeling. A key feature of hierarchical Bayesian models is that prior expectations regarding model structure are embedded in a probability model that reflects uncertainty about the form of the structure that links analytical units (such as geographic areas). This results in posterior estimates that are compromises between raw data summaries and estimates that conform exactly to the prior model structure. The posterior estimates are more precise and generally have lower mean-squared error than traditional data summaries, and yet are not strictly constrained to follow a posited prior model form.