An important distinction must be made in arguments that support the Bayesian way of accommodating evidence: the distinction between Bayes' theorem, as a mathematical given, and Bayes' rule, as a principle of coherence over time. The theorem is simply a mathematical relation among probability assignments,  \[ P(h \mid s) \; = \; P(h) \frac{P(s \mid h)}{P(s)} , \]  and as such not subject to debate. Arguments that support the representation of the epistemic state of an agent by means of probability assignments also provide support for Bayes' theorem as a constraint on degrees of belief. The conditional probability \(P(h \mid s)\) can be interpreted as the degree of belief attached to the hypothesis \(h\) on the condition that the sample \(s\) is obtained, as integral part of the epistemic state captured by the probability assignment. Bayes' rule, by contrast, presents a constraint on probability assignments that represent epistemic states of an agent at different points in time. It is written as  \[ P_{s}(h) \; = P(h \mid s) , \]  and it determines that the new probability assignment, expressing the epistemic state of the agent after the sample has been obtained, is systematically related to the old assignment, representing the epistemic state before the sample came in. In the philosophy of statistics many Bayesians adopt Bayes' rule implicitly, but in what follows I will only assume that Bayesian statistical inferences rely on Bayes' theorem.