As performed conventionally, nuclear probabilistic risk assessment (PRA) may be criticized as utilizing inscrutable and unjustifiably “precise” quantitative informed judgment or extrapolation from that judgment. To meet this criticism, controlling principles that govern the formulation of probability densities are proposed, given only the informed input that would be required for a simple bounding analysis. These principles are founded upon information theoretic ideas of maximum uncertainty and cover both cases in which there exists a stochastic model of the phenomenon of interest and cases in which these is no such model. In part, the principles are conventional, and such an approach is justified by appealing to certain analogies in accounting practice and judicial decision making. Examples are given. Appropriate employment of these principles is expected to facilitate substantial progress toward PRA scrutability and transparency.