Checking for Prior-Data Conflict

Inference proceeds from ingredients chosen by the analyst and data. To validate any inferences drawn it is essential that the inputs chosen be deemed appropriate for the data. In the Bayesian context these inputs consist of both the sampling model and the prior. There are thus two possibilities for failure: the data may not have arisen from the sampling model, or the prior may place most of its mass on parameter values that are not feasible in light of the data (referred to here as prior-data conflict). Failure of the sampling model can only be fixed by modifying the model, while prior-data conflict can be overcome if sufficient data is available. We examine how to assess whether or not a prior-data conflict exists, and how to assess when its effects can be ignored for inferences. The concept of prior-data conflict is seen to lead to a partial characterization of what is meant by a noninformative prior or a noninformative sequence of priors.