“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.

We consider the problem of variable selection for logistic regression when the dependent variable is measured imperfectly, under both differential and non-differential misclassification. An MCMC sampling scheme is designed, incorporating uncertainty about which explanatory variables affect the dependent variable and which affect the probability of misclassification. We assume that a small gold standard perfectly measured sample is available to augment the imperfectly measured sample, under the differential misclassification framework. A simulation study illustrates favourable results both in terms of variable selection and parameter estimation. Examples analysing the risk of violence against young women by their partner and the risk of injury in highway motor accidents are considered.