OBJECTIVE PRIOR DISTRIBUTIONS AND BAYESIAN UPDATING

For many years controversies have clouded constructive discussions between Bayesian and classical frequentistic schools of statistical inference. Much of the controversies have arisen because of mixing statistical variations with subjective distributions of belief. This paper points out parameter uncertainty distributions that have the frequency interpretation, and develops rules on how to select a prior density to obtain such objective posterior densities. It also shows how straightforward application of the Bayesian updating process in case of multivariate observables can lead to inconsistent results if the prior density is not firmly based on empirical evidence about the source population.