  When using complex Bayesian models to combine information, the checking for
consistency of the information being combined is good statistical practice.
Here a new method is developed for detecting prior-data conflicts in Bayesian
models based on comparing the observed value of a prior to posterior divergence
to its distribution under the prior predictive distribution for the data. The
divergence measure used in our model check is a measure of how much beliefs
have changed from prior to posterior, and can be thought of as a measure of the
overall size of a relative belief function. It is shown that the proposed
method is intuitive, has desirable properties, can be extended to hierarchical
settings, and is related asymptotically to Jeffreys' and reference prior
distributions. In the case where calculations are difficult, the use of
variational approximations as a way of relieving the computational burden is
suggested. The methods are compared in a number of examples with an alternative
but closely related approach in the literature based on the prior predictive
distribution of a minimal sufficient statistic.
