Power prior distributions for generalized linear models

In this article, we propose a class of prior distributions called the power prior distributions. The power priors are based on the notion of the availability of historical data, and are of great potential use in this context. We demonstrate how to construct these priors and elicit their hyperparameters. We examine the theoretical properties of these priors in detail and obtain some very general conditions for propriety as well as lower bounds on the normalizing constants. We extensively discuss the normal, binomial, and Poisson regression models. Extensions of the priors are given along with numerical examples to illustrate the methodology.