ABSTRACT

Reid and Cox [203] discuss the importance of statistical theory, in particular, “the foundations of statistical analysis, rather than the theoretical analysis of specific statistical methods.” Their essay makes a number of important points; we especially support their claim that calibration, or validity (in our IM language), is essential. However, it seems they dismiss the possibility that the inferential output can carry any meaningful probabilistic interpretation and, since a general strategy for constructing default priors remains elusive, they conclude that confidence-based methods are the most appropriate. This book has demonstrated that there is another alternativethe IM approach-and that it provides valid, prior-free probabilistic inference. As Brad Efron writes in his discussion of [262]: “Perhaps the most important unresolved problem in statistical inference is the use of Bayes theorem in the absence of prior information.” We interpret Efron’s comment as a challenge to develop a framework that provides meaningful probabilistic inference in the absence of prior information, thereby bridging the gap between frequentist and Bayesian thinking and solidifying the foundations of statistical inference. We believe that the IM framework is poised to meet this challenge, and we hope that the reader agrees.