Hidden Dangers of Specifying Noninformative Priors

“Noninformative” priors are widely used in Bayesian inference. Diffuse priors are often placed on parameters that are components of some function of interest. That function may, of course, have a prior distribution that is highly informative, in contrast to the joint prior placed on its arguments, resulting in unintended influence on the posterior for the function. This problem is not always recognized by users of “noninformative” priors. We consider several examples of this problem. We also suggest methods for handling such induced priors.