Practical problems associated with uninformative priors include the requirement that the posterior distribution be proper. The usual uninformative priors on continuous, unbounded variables are improper. This need not be a problem if the posterior distribution is proper. Another issue of importance is that if an uninformative prior is to be used routinely, i.e., with many different data sets, it should have good frequentist properties. Normally a Bayesian would not be concerned with such issues, but it can be important in this situation. For example, one would want any decision rule based on the posterior distribution to be admissible under the adopted loss function. Unfortunately, admissibility is often difficult to check, although some results are known (e.g., Berger and Strawderman 1996). The issue is particularly acute with hierarchical Bayes models; the usual priors (e.g., Jeffreys' prior) may give badly inadmissible decision rules if employed at the higher levels of the hierarchy.
