Recall that a prior probability distribution over statistical hypotheses expresses our uncertain opinion on which of the hypotheses is right. The central idea behind hierarchical Bayesian models (Gelman et al 2013) is that the same pattern of putting a prior over statistical hypotheses can be repeated on the level of priors itself. More precisely, we may be uncertain over which prior probability distribution over the hypotheses is right. If we characterize possible priors by means of a set of parameters, we can express this uncertainty about prior choice in a probability distribution over the parameters that characterize the shape of the prior. In other words, we move our uncertainty one level up in a hierarchy: we consider multiple priors over the statistical hypotheses, and compare the performance of these priors on the sample data as if the priors were themselves hypotheses.