Bayesian inference via a minimization rule
Stephen Graham Walker · Kent Academic Repository (University of Kent) · 2006
In this paper, we consider the Bayesian posterior distribution as the solution to a minimization rule, first observed by Zellner (1988). The expression to be minimized is a mixture of two pieces, one piece involving the prior distribution, which is minimized by the prior, and the other piece involves the data, which is minimized by the measure putting all the mass on the maximum likelihood estimator. From this perspective of the posterior distribution, Bayesian model selection and the search for an objective prior distribution, can be viewed in a way which is different from usual Bayesian approaches.