Jerzy Neyman Research Paper

After teaching in Warsaw and Cracow, Neyman obtained a postdoctoral fellowship to study under Karl Pearson at University College, London in 1925, where he first met some of the leading statisticians of his day, including W. vs. Gosset (‘Student’), R. A. Fisher, and Egon vs. Pearson (the son of Karl Pearson, and an important statistician in his own right). The next year Neyman then obtained a fellowship from the Rockefeller Foundation and studied in Paris, attending mathematical lectures by Borel, Lebesque, and Hadamard. During the summer of 1927 Neyman returned to Poland, and resumed teaching at the Universities of Warsaw and Cracow.

From 1928 to 1934 Neyman remained in Poland, working in both applied and mathematical statistics. He pursued a broad range of applied statistical interests in agriculture, biology, chemistry, and socioeconomics, ultimately leading to his appointment as head of the Statistical Laboratory of the Nencki Institute of Experimental Biology. But at the same time Neyman also continued to collaborate with Egon Pearson, work that was to result in some of their most important papers on the theory of statistical tests.

In 1933 Karl Pearson retired as Professor of Statistics from University College. Although Fisher was Pearson’s obvious choice as successor, the two had for more than a decade been bitter enemies and, in Solomon fashion, it was decided to divide the Department in two: a Department of Genetics to be headed by Fisher (as Professor of Genetics), and a Department of Applied Statistics to be headed by Egon Pearson. Not unnaturally, Egon Pearson immediately invited his collaborator and friend Neyman to join him at University College in the new Department of Statistics, initially as a Senior Lecturer and later as Reader. Neyman accepted Pearson’s offer, a decision that was to have profound consequences for his career.

Despite the tensions that immediately arose between the two Departments, Neyman initially remained on cordial terms with Fisher (as evidenced both in their personal correspondence and their 1934 exchange at a meeting of the Royal Statistical Society during the discussion of Neyman’s paper on confidence intervals). But their personalities and scientific philosophies were so different that conflict between the two was inevitable. Neyman’s paper (1935) on the design of experiments (which implicitly criticized some of Fisher’s most important work) enraged Fisher, and the clash between the two during the discussion of Neyman’s paper led to a complete and permanent severing of relations between them. (Neyman’s unfortunate 1961 retrospective polemic provides a useful illustration of just how bitter the dispute between the two became, although it exaggerates Fisher’s role prior to the 1950s: after the first several years, Fisher largely ignored Neyman in print rather than attacking him until the middle of the 1950s.)

In 1937 Neyman toured the USA, lecturing both at the U S Department of Agriculture (at the invitation of E. Deming) and a number of major universities, resulting in the offer of a position at the University of California at Berkeley. Attracted by the opportunity to build from the ground up a statistical group, Neyman accepted the offer and permanently left London for Berkeley in 1938.

Over the next several decades Neyman used his intellectual gifts, force of personality, and international standing in the statistical community to make the University of California at Berkeley one of the leading centers of statistical research in not just the USA, but the world. In 1955 the continuing expansion of Neyman’s Statistical Laboratory led to the formation at Berkeley as an independent Department of Statistics.

Throughout his career at Berkeley Neyman continued to vigorously promote statistics at the international level as well in the USA; particularly noteworthy in this regard being the institution of the Berkeley Symposia on Probability and Mathematical Statistics, held every five years from 1945 until 1970. International visitors also came to Berkeley on a regular basis, such visits often either arranged by, or due to Neyman.

During his long life Neyman received numerous honors, many of these coming after his retirement in 1961. (The retirement was in name only. In an unusual exception to Berkeley’s rules regarding Emeritus status, Neyman was permitted to continue as Director of the Statistical Laboratory.) In addition to being elected a member of the National Academy of Sciences in 1964, Neyman was also elected as a foreign member of the Royal Society, and the Polish and Swedish Academies of Science. Other honors included medals (the US Medal of Science and the Guy Medal in gold of the Royal Statistical Society), and honorary doctorates (from Berkeley, the University of Chicago, the University of Warsaw, the University of Stockholm, and the Indian Statistical Institute).

Neyman remained active to the end, running a weekly seminar at which many of his visitors and guests spoke. He died in Berkeley, California on August 5, 1981, after a brief illness.

2. Scientific Contributions

2.1 Hypothesis Testing

Although Neyman wrote papers in several areas both prior to his collaboration with Egon Pearson, and after his departure for the USA, the decade from 1928 to 1938, when he collaborated with Pearson, marked the period of his most important and lasting contributions to statistics. The first of these (Neyman and Pearson 1928) introduced the concepts of two types of error (type one and type two error), and the likelihood ratio, using the latter to derive as special cases some of the standard tests then in use. Ironically, in the light of Neyman’s later violent opposition to Bayesian methods, Pearson refused to be the co-author of a second paper, drafted by Neyman (1929), because it appealed to the use of prior probabilities. Despite this disagreement, however, their collaboration continued, and in the short period of six years (from 1933 to 1938) they proceeded to lay the foundations of the modern theory of hypothesis testing.

The paper of Neyman and Pearson (1933) on statistical tests, formalized the process of hypothesis testing by providing a clear mathematical framework. In the case of simple hypotheses the Neyman–Pearson lemma was stated and proved; and in the case of composite hypotheses the concepts of similar and best critical regions were introduced. Then, in a pair of papers that appeared in 1936 they further advanced the theory by introducing the concept of unbiased critical region and illustrated the use of power curves to compare tests (Neyman and Pearson 1936a). They then discussed the role of sufficient statistics and the novel concept of uniformly powerful tests (Neyman and Pearson 1936b). Finally, in a last paper (Neyman and Pearson 1938) they returned to the question of the existence of unbiased critical regions.

2.2 Statistical Estimation

Neyman introduced the terminology of confidence interval, in his 1934 paper on sampling (Neyman 1934). Originally Neyman deferred to Fisher’s priority (Fisher 1930) in discovering the basic underlying idea (that one could find sets having coverage probabilities independent of the parameter being estimated). But after his break with Fisher, faced both with Fisher’s criticism and indeed denial that Neyman’s confidence intervals were fiducial intervals at all, Neyman proceeded on his own path, developing a complete theory of confidence intervals (Neyman 1937).

2.3 Other Work

Neyman made many other important contributions to mathematical and applied statistics. Notable examples include his work on sampling theory, in particular what is currently termed Neyman allocation in stratified sampling (Neyman 1938). (Neyman notes in the introduction to the paper that the problem was posed to him during his lectures in 1937 at the US Department of Agriculture, one of the proposes being Milton Friedman) Other contributions included the so-called ‘smooth’ goodness of fit tests, models for contagion, BAN (best asymptotically normal) estimation, and so-called C(α) optimal tests of composite hypotheses. Much of his later work was applied and done in collaboration with his long-time colleague and friend, Elizabeth Scott.

3. Influence

It would be hard to overstate the impact that Neyman had on both the subject of modern statistics and the statistical profession. Although the English school of statistics, led (among others) by Galton, Karl Pearson, Weldon, Edgeworth, Gosset, Yule, and Fisher, both transformed the subject and vastly extended its scope, the process was undoubtedly hindered by concerns and doubts regarding both its conceptual underpinnings and rigorous mathematical structure. By advancing a purely frequentist setting for the subject, Neyman made the subject palatable to those suspicious of its Bayesian roots; and by presenting it as a natural branch of modern mathematics, using precise definitions and presenting many of its problems in purely mathematical guise, Neyman made it an attractive area of research for many mathematicians.

This phenomenon was particularly striking in the theory of confidence intervals. Fisher’s 1930 paper, ‘Inverse Probability’, in which the term ’fiducial probability’ first appears, presents, in all essential respects, a general theory of confidence intervals for the one parameter case. (Fisher noted that in a wide class of cases the probability integral transformation could be inverted to provide a parameter-independent probability statement concerning intervals containing the parameter; the theory presented by Fisher even contained a sample theory interpretation of the probability in question.) But, approaching the subject from the perspective of inductive inference (as opposed to what Neyman later termed ‘inductive behavior’),

Fisher perceived difficulties in the extension of his approach to the multi-parameter case. Neyman, in contrast, abstracting out what he believed to be the mathematical essentials of the problem (the construction of sets that would contain a parameter with a long-term frequency independent of all unknown parameters), saw no difficulties in such an extension and proceeded to propose one in his 1934 paper. Fisher’s subsequent attacks and insistence that Neyman’s confidence intervals were not fiducial intervals in the sense intended by Fisher were then seized on by Neyman, who was quite content from then on to portray his own theory as one clearly different from Fisher’s. (It is indicative of the magnitude of the break between the two that is his 1937 memoir on confidence intervals, Neyman not only did not cite Fisher’s 1930 paper, but in a final footnote asserted that he had independently discovered the confidence interval arising from the t-statistic in 1930.) The conceptual and mathematical clarity of Neyman’s approach eventually triumphed in statistical practice and textbook presentations (although even today the tension between the two approaches continues in the guise of the conflict between conditional and unconditional inference).

Similarly, the mathematical elegance and clarity of the Neyman-Pearson theory of tests made it the standard mode of presentation of the subject in many statistical textbooks despite Fisher’s equally vehement opposition. (Fisher believed in, and indeed played a crucial role in the development of statistical tests of significance for a single null hypothesis, but thought that when more than one hypothesis was in question, parameter estimation rather than hypothesis testing was indicated.)

Closely tied to the acceptance of Neyman’s approach was his impact on the statistical profession, especially in the USA. Under Neyman’s leadership, the Berkeley Statistical Laboratory attracted and trained many of the leading figures in mathematical statistics in the decades immediately after the war, including (to name only a few) Erich Lehmann, Joseph Hodges, David Blackwell, Henry Scheffe, and Lucien Lecam.

Many of Neyman’s papers from 1923 to 1945 are conveniently collected in two volumes published in 1967 by the University of California Press, Berkeley and Los Angeles: A Selection of Early Statistical Papers of J. Neyman, and Joint Statistical Papers by J. Neyman and E. vs. Pearson.

Bibliography:

1. Fisher R A 1930 Inverse probability. Proc. Camb. Phil. Soc. 26: 528–35
2. Neyman J 1934 On the two different aspects of the representative method: The method of stratified sampling and the method of purposive selection. J. Roy. Soc. Ser. A. 97: 558–625
3. Neyman J 1935 Statistical problems in agricultural experimentation (with K. Iwaskiewicz and St. Kolodziejczyk). J. Roy. Soc. Ser. B. Suppl. 2: 107–80
4. Neyman J 1937 Outline of a theory of statistical estimation based on the classical theory of probability. Philosophical Transactions of the Royal Society of London, Series A 236: 333–80
5. Neyman J 1938a Contributions to the theory of sampling human populations. Journal of the American Statistical Association 33: 101–16
6. Neyman J 1952 Lectures and Conferences on Mathematical Statistics and Probability 2nd ed., rev. and enl. Graduate School, US Department of Agriculture, Washington, DC
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