Mathematical Statistics and the ISI (1885-1939) Stephen M. Stigler University of Chicago, Department of Statistics 5734 University Avenue Chicago IL 60637, USA [email protected] 1. Introduction From its inception in 1885, the International Statistical Institute took all of statistics as its province. But the understood meaning of “statistics” has undergone significant change over the life of the Institute, and it is of interest to inquire how that change, whether evolutionary or revolutionary, has been reflected in the business of the Institute, in its meetings and its membership. I propose to consider this question in regard to one particular dimension, that of mathematical statistics, and one particular period, that from the rebirth of international statistics in 1885 until the eve of World War II. Mathematical statistics has been a recognized division of statistics at least since the 1860s, when Quetelet at the Congress in the Hague admonished the assembled statisticians not to divide the école mathématique from the école historique, but to take statistics whole, to open the doors to statistics in the broadest sense in all its flavors (Stigler, 2000). But even with this recognition, mathematical statistics only emerged as a discipline later. I have argued elsewhere that this emergence can be dated to the year 1933, and even if one thinks that date absurdly precise, there was a distinct and palpable change that was evident around that time (Stigler, 1999, Ch. 8). It was then that changes initiated a half-century earlier by Galton and Edgeworth and developed subsequently by Karl Pearson and Udny Yule, were seized upon and transformed by Ronald Fisher and Jerzy Neyman and Egon S. Pearson, and the intellectual practices of all of statistics were changed forever. How were these epochal changes reflected in the ISI? The impact of any such change upon a society would be expected to be most directly reflected in its publications and meetings. Early in the 1930s the Royal Statistical Society initiated a series of review papers intended to summarize the exciting new work in mathematical statistics, but it was not long before they recognized this work was developing so rapidly and extensively that they could not keep up with it in this way, and by the mid-1930s they opened the gates of their journal to the work itself. The American Statistical Association reacted by helping to found a new journal, the Annals of Mathematical Statistics, and while a budgetary crisis soon led them to abandon this offspring, with wise leadership it managed to create a new sponsoring society in 1935, the Institute of Mathematical Statistics, and the Annals flourished in this new home. But what of the ISI? 2. The ISI before 1939 Mathematical statistics was not entirely absent from the publications of the ISI before 1939, but it was nearly absent. In the entire period there was scarcely any evidence of the new and energetic development of mathematical statistics in the publications of the ISI. The one substantial article on mathematical statistics in the ISI Bulletin was “Contribution to the theory of certain test criteria,” published by Jerzy Neyman in 1929, nineteen years before Neyman was elected to membership. There were a very few other works of mathematical interest: In 1936 Georges Darmois published an expansion on an influential article he had published the year before in the Comptes Rendus de l’Académie des Sciences de Paris (Darmois, 1935, 1936), an article that developed the relationship of sufficient statistics to the exponential family and is today remembered in the phrase “Darmois-Koopman Theorem,” or sometimes the “Fisher-Darmois-Koopman-Pitman Theorem,” it being generally agreed that this is a classic case of simultaneous independent discovery, since the latter three authors were operating independently, all being aware of Fisher’s earlier work. Barankin and Maitra (1963) discuss the distinctions among the works. And Cornish and Fisher (1937) published the expansion that bears their name, notwithstanding its anticipation by Theile in 1899 (Lauritzen, 2002). Aside from these, there were a small handful of shorter or less- developed articles that reviewed other mathematical work, such as articles by J. O. Irwin on factor analysis (1934) and Octav Onicescu on Markov chains (1936). In 1934 Maurice Fréchet orchestrated a “report” on the use of the correlation coefficient, and he took the opportunity to publish several correspondents’ reactions to a deliberately provocative paragraph he circulated endorsing the coefficient and suggesting that the values .30 and .50 for r could be taken as limits separating non-existent, weak, and strong relationships between two variables (Frechét (1934), Armatte, 2001). Nearly all of the correspondents (including Fisher, Hotelling, Gini, Rietz, von Mises, Frisch, Gumbel) found the statement wanting in some respect. Fisher’s contribution summarized the history of what we now tend to call Pearson’s r, as “the product moment coefficient used by Bravais, and later introduced by Pearson in connection with the researches of Francis Galton.” Fréchet took the hint and subsequently referred to r as “the Bravais-Galton coefficient.” All of this is interesting reading, and the report may have been quite useful for the ISI members, but it was neither novel mathematics nor statistics, even in 1934. 3. The reason mathematical statistics was largely absent The 1920s and 1930s were a period of exciting development in mathematical statistics. Why was there so little evidence of this in the ISI? The ISI did count among its members several who contributed to this development. When the ISI was created in 1885, some members of the older schools were among the first members: Wilhelm Lexis and J. B. J. Liagre. Between 1886 and 1905, Francis Galton, Francis Edgeworth, Arthur Bowley, Ladislaus von Bortkiewicz, and G. Udny Yule were elected members. By 1927 they were joined by A. A. Tchouprov [Chuprov], George Knibbs, Emile Borel, Irving Fisher, and David Heron, all men who could be expected to appreciate mathematical work and at least occasionally contribute to it. They were followed by R. A. Fisher and Maurice Fréchet in 1931, Georges Darmois in 1935, and E. S. Pearson and P. C. Mahalonobis in 1937. These people were all quite formidable mathematical talents, but the most revealing aspect of this list is those whose names are not on it: Karl Pearson, Harold Jeffreys, A. A. Kolmogorov, Joseph Doob, Abraham Wald, Harald Cramér, Daniel Dugué, Maurice Bartlett, Harold Hotelling, William Cochran, Samuel S. Wilks, Walter Shewhart, and even Jerzy Neyman. All of these were writing important articles in mathematical statistics before 1937. Most of them were elected members in the decade 1947-1957, after the ISI resumed meetings following World War II, and Wald would surely have been elected had he not died in December 1950 (Neyman had nominated him and was actively campaigning for his admission). Only Karl Pearson and Harold Jeffreys among the names on this list were never members of the ISI. This list of names suggests a principal reason that the ISI was so slow in noticing, much less adopting and extending the new mathematical approaches. The ISI was conceived of in 1885 as an elite organization, and election was taken quite seriously. This had the advantage of guaranteeing the intellectual strength and stability of the organization. But it had one unfortunate consequence: If only well-established scholars were elected, then there would be a consequent delay in inducting young workers in new areas. Even those few among the new generation of mathematical statisticians who were members, like Fisher after 1931, would not have found the broad senior membership of the ISI, with a strong emphasis on national and economic statistics, an ideal audience for their more mathematical work, and the publishing delays (two to four years for the Bulletin in the mid-1930s) would not have been an attraction. The experience of the International Congresses of Mathematicians, held every four years but without elected membership, was to a degree different from that of the ISI. There, over the same period there was somewhat more evidence of mathematical statistics than in the ISI (Krengel, 1997). Most of this was on probability, but these Congresses also witnessed some important works on statistics, including by Fisher and by Neyman. While the traces of mathematical statistics in the publications and proceedings of the ISI before World War II were barely detectable, there was nonetheless great vitality in the meetings and much else of methodological interest, particularly as regards sampling. One particularly important line of work was initiated by A. Kiaer in 1895 under the title Representative Sampling and developed mostly within the ISI. The story of this development and the surrounding debates is told in great and interesting scholarly detail by Kruskal and Mosteller (1980). 4. After the war The ISI was essentially inactive between 1938 and 1947. The Prague session closed prematurely on its second day, September 13, 1938; Hitler’s speech of September 12 on German claims to portions of Czechoslovakia had precipitated the crisis that would lead to Chamberlain’s ill-fated trip to Munich September 15. In 1947 the meetings resumed in New York (Nixon, 1960). With the renewal of meetings came a renewal of spirit, and an influx of new members. Jerzy Neyman was elected in 1948 and was to play a vital role in finally bringing mathematical statistics to play an active role in the ISI. Neyman worked to nominate and elect new members, including some of the most active younger mathematical statisticians, and he was instrumental in starting the movement in 1958 that was to result eventually in the founding of the Bernoulli Society in 1975 (Teugels, 2000, 2001). The number of ISI members more than doubled in the decade following the 1947 session, and this new blood would help produce a period of great excitement and growth in international statistics.