A somewhat different problem is that the Bayesian formalism, in particular its use of probability assignments over statistical hypotheses, suggests a remarkable closed-mindedness on the part of the Bayesian statistician. Recall the example of the foregoing, with the model \(M = \{ h_{1/2}, h_{3/4} \}\).  The Bayesian formalism requires that we assign a probability distribution over these two hypotheses, and further that the probability of the model is \(P(M) = 1\). It is quite a strong assumption, even of an ideally rational agent, that she is indeed equipped with a real-valued function that expresses her opinion over the hypotheses. Moreover, the probability assignment over hypotheses seems to entail that the Bayesian statistician is certain that the true hypothesis is included in the model. This is an unduly strong claim to which a Bayesian statistician will have to commit at the start of her analysis. It sits badly with broadly shared methodological insights (e.g., Popper 1934/1956), according to which scientific theory must be open to revision at all times (cf. Mayo 1996). In this regard Bayesian statistics does not do justice to the nature of scientific inquiry, or so it seems.