Researchers in the field of computational psychiatry have recently sought to model the formation and retention of delusions in terms of dysfunctions in a process of hierarchical Bayesian inference. I present a systematic review of such models and raise two challenges that have not received sufficient attention in the literature. First, the characteristic that is supposed to most sharply distinguish hierarchical Bayesian models from their competitors is their abandonment of the distinction between perception and cognition in favour of a unified inferential hierarchy. Standard ways of characterising this hierarchy, however, are inconsistent with the range of phenomena that delusions can represent. Second, there is little evidence that belief fixation in the healthy population is Bayesian, and an apparent abundance of evidence that it is not. As such, attempts to model delusions in terms of dysfunctions in a process of Bayesian inference are of dubious theoretical value.