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'LVFXVVLRQIRU,6,+LVWRU\6HVVLRQ,30 Stephen M. Stigler Helsinki, August 12, 1999 The three speakers today have cogently argued that Scandinavian statistics can boast an excellence second to none; more than that they have actually demonstrated this excellence through the quality of their presentations. I will raise a few questions and suggest a few qualifications, but the main thrust of their argument is undeniable: There has been a rich and continuing history of important statistical work of all types in the Scandinavian countries, and it is good that it is receiving the historical attention it deserves. Let me proceed chronologically, starting with the paper of Georg Luther. The story of official statistics in Sweden in the 18th century was new to me, and it is most interesting. Several of the arguments presented here have, I suspect, even broader applicability. For example, the relationship of the growth of official statistics to the needs of empire must be quite general. So too the development of accurate vital records – birth and mortality statistics – seems to be tied to the development of a strong and unified church. Both of these would reward further study, and a natural question is, to what degree were these developments spontaneously responding to internal needs, and to what degree were they reflecting instances of imported technology? Were the Swedish parish records consciously modeled after London’s parish-based Bills of Mortality, or were they an independent innovation? Also, the tendency for the persistence of good statistical administration once established is not unique to this part of the world. For example, Australia has had a similar experience, somewhat later than Sweden. I might note that this persistence is also testified to through Professor Schweder’s paper, where several of the individuals discussed may be seen as heirs to the earlier tradition of excellence in Swedish insurance. One question I would pose to Dr. Luther: The paper discusses at least four different areas where excellent official (or at least institutional) statistics developed at roughly the same time, and all were in Sweden. Was there any move at that time that would signal a recognition by those involved that these areas were intellectually connected? For example, was there any move toward a unification of some or all of these efforts in one statistical agency? Tore Schweder has given us a wonderful brief tour of a stellar cast of Scandinavian statisticians. One need not accept his conclusion (that the Scandinavians matched Galton and his British contemporaries) to applaud the achievements of this group. For my part, I believe the Scandinavians surpassed the British in some respects, fell far behind in others, and in any case statistics is fortunately a cooperative enterprise: there is no World’s Cup in statistics. All of the names Tore lists seem to belong properly to the population of extraordinary statisticians worthy of our applause; several (Sundt, Fibiger, Hjort) were new to me. Tore mentions that the choices for inclusion were subjective. I would only point to one omission: I think that Kirsten Smith deserves inclusion. She was a student of Thiele’s who made important contributions independently, even publishing in Biometrika. She was a pioneer in the design of experiments for regression analysis, and was an influential stimulus to Fisher in his early development of parametric inference. I would like to know more about her. Of the names Tore does include, some seem to have a common thread, through their work being inspired by problems in insurance and forestry. Some on Tore’s list have been widely recognized by having their names enshrined as eponyms: Gram, Charlier, Erlang, and Lindeberg are words familiar to recent generations of statisticians even if the men behind those names are not. Curiously, of the names in Tore’s Who’s Who, only Anders Kiaer played a prominent role in the ISI (for an excellent discussion of Kiaer’s work, see Kruskal and Mosteller, 1980). This brings me to the final name on Tore’s list and the entire focus of Steffen Lauritzen’s paper, to the remarkable Danish applied mathematician Thorvald Nicolai Thiele. Thiele has received scant historical notice over the past century, at least until papers by Anders Hald and Steffen Lauritzen in 1981 on the man and his work. Thiele clearly had a first-rate statistical mind, and the planned publication by Steffen Lauritzen of an English translation of Thiele’s major book is most welcome. Why has his work been so neglected? The fact that the work was published in Danish is frequently mentioned as a reason, but that cannot be the only reason and I suspect it is not the major one. In the first place, Thiele has been neglected by Scandinavian statisticians as much as – or perhaps more than – by English statisticians. It is true that Karl Pearson and Ronald Fisher cited Thiele only briefly and grudgingly, but on the other hand, Charlier in a 1910 book on mathematical statistics barely mentions Thiele, Cramér in his great 1944 book makes only the briefest of mentions of Thiele, and Hald himself in his important 1952 book does not cite Thiele at all. In contrast, in 1931 the Americans reprinted Thiele’s entire 1903 book in a major journal, but no noticeable increase in citations followed. I suspect that one major reason for Thiele’s neglect is that he is exceedingly hard to read in any language, as both Hald and Lauritzen clearly state. Presentation does matter. As evidence on this I would note that while two of today’s papers remark that Thiele had introduced the additive model for a two way layout in 1889, they do not mention that four years earlier Francis Edgeworth had also introduced this model, and at least in some respects gone further in its analysis than did Thiele. Edgeworth wrote in English, in the Journal of the Royal Statistical Society (hardly an obscure journal), yet this work of Edgeworth’s has been as much – or more – neglected than Thiele’s, even in England. Fisher was grudging in his citation of Thiele, to the point of strongly (and in the end successfully) insisting upon the term “cumulant” rather than Thiele’s “semi-invariant” or “half- invariant”, in the face of Ragnar Frisch’s strong resistance. (Incidentally, the term “cumulant” had been suggested to Fisher by Harold Hotelling.) There seems to be no doubt that where Fisher’s work crossed Thiele’s, Fisher had proceeded initially in ignorance of Thiele. Later he never did take Thiele’s full measure, relying mostly on the only works of Thiele available in English. Indeed, in 1932 Fisher wrote to a British colleague that translation could be ruinous to a reputation in science, where, unlike poetry, one could not “claim that the original merit is ten times that of any translation.” In his letter Fisher stated that, “If Thiele, for example, had never published his 1903 volume in English, we might still be burning Joss sticks to his name.” Fisher’s disregard for Thiele would have been encouraged by their quite different conceptual approaches: I do not see even a hint of Fisher’s parametric families in Thiele. Thankfully, due to the efforts of Lauritzen and others, Thiele has now not only been fully translated both into English, but (I think more importantly) into clear mathematical and statistical language where we, unlike Fisher, can take his full measure and understand just how far he did see. The fact that the very mathematical and statistical language we use in this assessment owes much to British and other statisticians should not prevent our enthusiastically celebrating the excellence of Scandinavian statistics this afternoon. 5HIHUHQFHV Smith, Kirsten (1918). On the standard deviations and interpolated values of an observed polynomial function and its constants and the guidance they give towards a proper choice of the distribution of observations. Biometrika 12: 1-85. Kruskal, William H., and Frederick Mosteller (1980). Representative sampling IV. International Statistical Review 48: 169-195. Stigler, Stephen M. (1978). Francis Ysidro Edgeworth, statistician. Journal of the Royal Statistical Society (Series A) 141: 287-322..

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