On the non-arbitrary assignment of equi-probable priors

Abstract

How to form priors that do not seem artificial or arbitrary is a central question in Bayesian statistics. The case of forming a prior on the truth of a proposition for which there is no evidence, and the definte evidence that the event can happen in a finite set of ways, is detailed. The truth of a propostion of this kind is frequently assigned a prior of 0.5 via arguments of ignorance, randomness, the Principle of Indiffernce, the Principal Principal, or by other methods. These are all shown to be flawed. The statistical syllogism introduced by Williams in 1947 is shown to fix the problems that the other arguments have. An example in the context of model selection is given.