It is a privilege to have the chance of congratulating Professor Efron first on this wise paper, then on the richly merited International Prize, the award of which the paper commemorates, but above all on the whole body of his deeply impressive, wide-ranging contributions to our subject.
One issue which the paper indirectly raises is the role of different approaches to the conceptual and mathematical theory of our field. One of the appeals of the field is its totally international character yet, inevitably, broad and hazily defined national contrasts are visible.
Thus Professor Efron links “traditional” statistical theory to Neyman and Pearson. Yet the two set out to clarify earlier work of R.A. Fisher, first with Fisher’s encouragement, which only later turned to destructive hostility. The mathematical clarity of Neyman’s work is, of course, appealing but it may be argued that its overformalization continues to lead to misunderstanding, unproductive discussion and rigidity concerning, in particular, the role of significance tests.
The Nordic approaches have made an important and distinctive contribution to the field. See, in particular, the recent fine account of Rolf Sundberg, Statistical modelling by exponential families, stemming from the much earlier contribution of Per Martin-Lof. In the UK, Egon Pearson played a distinctive role in the development of our subject. He mostly had a preference for numerical illustration and was deeply involved in applications, stemming in part from an early visit he made to Bell Labs.
One of the great masterpieces of our field, largely unread nowadays, is M.S. Bartlett’s (1958) Introduction to stochastic processes and their application and Bartlett’s influence on statistical development, at least in UK, was second only to Fisher’s. See, for example, his treatment in 1937 of asymptotic theory in which the dimension of the parameter space increases proportionally to sample size. One of the themes of his wide-ranging work was the use of specific stochastic processes, Markov chains, generalized birth-death processes and others, for the detailed interpretation of biological or physical science data; his final post was as Professor of Biomathematics. An aspect of both Fisher’s and Bartlett’s work, which I must admit I admire, is a total lack of concern with formal mathematical regularity conditions which, of course subject to due care, typically contribute little to understanding. Professor Efron in his theoretical papers manages with great skill and panache to combine careful mathematical discussion with judicious statistical emphasis. Special stochastic models probably tend nowadays to be treated much more often by computer simulation than by mathematical analysis of the differential equations involved with obvious gains and some loss, especially when the model is intended to lead to semi-qualitative understanding of an empirical phenomenon. The aethos is rather different from the use of families of regression-type models and even more so from that of machine learning, the latter achieving very specific purposes often with high effectiveness, as Professor Efron’s discussion so elegantly illustrates. But how useful are they as a guide to deeper interpretation or for broader context prediction?
I reemphasize my admiration for Professor Efron’s work and for this paper.