I recently read George Box’s paper “Sampling and Bayes’ Inference in Scientific Modelling and Robustness” (JRSSA, 1980). It’s a discussion paper, and I really liked his rejoinder. It starts like this:

“To clear up some misunderstandings and to set my reply in context, let me first make clear what I regard as the proper role of a statistician. This is not as the analyst of a single set of data, nor even as the designer and analyser of a single experiment, but rather as a colleague working with an investigator throughout the whole course of iterative deductive-inductive investigation. As a general rule he should, I think, not settle for less. In some examples the statistician is a member of a research team. In others the statistician and the investigator are the same person but it is still of value to separate his dual functions. Also I have tended to set the scene in the physical sciences where designed experiments are possible. I would however argue that the scientific process is the same for, say, an investigation in economics or sociology where the investigator is led along a pat, unpredictable a priori, but leading to (a) the study of a number of different sets of already existing data and/or (b) the devising of appropriate surveys.

The objective taking precedence over all others is that the scientific iteration converge as surely and as quickly as possible. In this endeavour the statistician has an alternating role as sponsor and critic of the evolving model. Deduction, based on the temporary pretense that the current model is true, is attractive because it involves the statistician in “exact” estimation calculations which he alone controls. By contrast induction resulting on the idea that the current model may not be true is messy and the statistician is much less in control. His role is now to present analyses in such a form, both numerical and graphical, as will accurately portray the current situation to the investigator’s mind, and appropriately stimulate his colleague’s imagination, leading to the next step. Although this inductive jump is the only creative part of the cycle and hence is scientifically the most important, the statistician’s role in it may appear inexact and indirect.

If he finds these facts not to his liking, or if his training has left him unfamiliar with them, the statistician can construct an imaginary world consisting of only the clean deductive half of the scientific process. This has undoubted advantages. A model dubbed true remains so, all alternative models are known a priori, the likelihood principle and the principle of coherence reign supreme. It is possible to devise rigid “optimal” rules with known operating characteristics which aspire to elevate the statistician from a mere subjective artist to an objective automaton. But there are disadvantages. Deduction alone is sterile–by cutting the iterative process in two you kill it. What is left can have little to do with the never-ending process of model evolution which is the essence of Science.”