Weak Informativity and the Information in One Prior Relative

A question of some interest is how to characterize the amount of information that a prior puts into a statistical analysis. Rather than a general characterization of this information, we provide an approach to characterizing the amount of information a prior puts into an analysis, when compared to another base prior. The base prior is considered to be the prior that best reflects the current available information. Our purpose then, is to characterize priors that can be used as conservative inputs to an analysis, relative to the base prior, in the sense that they put less information into the analysis. The characterization that we provide is in terms of a priori measures of prior-data conflict.