Bayes’ Rule, Principle of Indifference, and Safe Distribution

Abstract

Bayes’ rule is the basis of probabilistic reasoning. It enables to surmount information gaps. However, it requires the knowledge of prior distributions of probabilistic variables. If this distribution is not known then, according to the principle of indifference, the uniform distribution has to be assumed. The uniform distribution is frequently and heavily criticized. The paper presents a safe distribution of probability density that can be often used instead of the uniform distribution to surmount information gaps. According to the authors’ knowledge the concept of the safe distribution is new and unknown in the literature.