Discussion of “ Statistical Inference : The Big Picture ” by R . E . Kass Hal

Rob Kass presents a fascinating vision of a “post”Bayes/frequentist-controversy world in which practical utility of statistical models is the guiding principle for statistical inference. I agree with Kass on many points. In particular, Kass is correct (in my opinion) when he notes that much modern statistical work develops statistical models (the theoretical world) and asks whether the models provide a reasonable description or explanation of data (the real world). A recent example in my own collaborative work (Scharenbroich et al., 2009) builds a storm tracking model that combines subjective information from climate scientists about storms in the eastern Pacific and historical data to develop a probabilistic model that appears to fit data well. A critical element of this approach, as Kass notes, is that we understand the assumptions that underlie our statistical model and, equally important, that we subject these assumptions to careful scrutiny. I continue to find posterior predictive model checks (Gelman, Meng and Stern, 1996) especially helpful for assessing model fit. Of course, this would not be a particularly interesting discussion if it focused on points of agreement. I believe that Kass’s proposed “big picture” fails at one key goal that we should have for such a picture—it does not easily illustrate one of the key concepts of the field, the art of generalizing from sample data to larger populations. I argue below that the “old” big picture (Kass’s Figure 3) still has great value for me and for the field. I also speculate a bit about pragmatism as a foundation on which to build a training program for statisticians.