# Neyman, Jerzy

# NEYMAN, JERZY

(*b*. Bendery, Russia, 16 April 1894; *d*. Berkeley, California, 5 August 1981)

*statistics*.

**Early Years** , Jerzy Neyman was born in Bendery, Russia, to parents of Polish ancestry, His full name with title, Splawa-Neyman, the first part of which he dropped at age thirty, reflects membership in the Polish nobility, Neyman’s father, Czeslaw, who died when Jerzy was twelve, was a lawyer and later a judge, and an enthusiastic amateur archaeologist. Since the family had been prohibited by the Russian authorities from living in central Poland, then under Russian domination, Neyman grew up in Russia: in Kherson, Melitopol, Simferopol, and (after his father’s death) in Kharkov, where in 1912 he entered the university.

At Kharkov, Neyman, was first interested in physics, but because of his clumsiness in the laboratory abandoned it in favor of mathematics. He was greatly struck by Henri Lebesgue’s Leçons sur l’intélgration et la recherche des functions primitives, “the most beautiful monograph that I ever read” as he called it many years later. A manuscript on Lebesgue integration (530 pages, handwritten) that he submitted to a prize competition won a gold medal.

One of his mentors at Kharkov was Sergei Bernstein, who lectured on probability theory and statistics (including application of the latter to agriculture), subjects that did not particularly interest Neyman. Nevertheless he later acknowledged the influence of Bernstein, from whom he “tried to acquire his tendency of concentrating on some ‘big problem’”. It was also Bernstein who introduced him to Karl Pearson’s *The Grammar of Science*, which made a deep impression.

After World War I, poland regained its independence but soon became embroiled in a war with Russia over borders. Neyman, still in Kharkov, was jailed as an enemy alien. In 1921, in an exchange of prisoners, he finally went to Poland for the first time, at the age of twenty-seven.

In Warsaw he established contact with Waclaw Sierpiński, one of the founders of the journal *Fundamenta Meathematicae*, which published one of Neyman’s gold medal results (**5** [1923], 328–330). Although Neyman’s heart was in pure mathematics, the statistics he had learned form Bernstein was more marketable and enabled him to obtain a position as (the only) statistician at the agricultural institute in Bydgoszcz (formerly Bromberg). There, during 1921 and 1922, he produced several papers on the application of probabilistic ideas to agricultural experimentation. In the light of Neyman’s later development, this work is of interest because of its introduction of probability models for the phenomena being studied, more particularly a randomization model for the case of a completely randomized experiment. (For more details of Neyman’s treatment, see Scheffé, *Annals of Mathematical Statistics*, **27** [1956;], 269.) He had learned the philosophy of such an approach from Pearson’s book, which laid great stress on models as mental constructs whose formulation constitutes the essence of science.

In December 1922 Neyman gave up his job in Bydgoszcz to take up a position at the State Meteorological Institute, a change that enabled him to move to Warsaw. He did not like the work—being in charge of equipment and observations—and soon left this position to become an assistant at the University of Warsaw and special lecturer in mathematics and statistics at the Central College of Agriculture; he also gave regular lectures at the University of Kraków. In 1924 he obtained his doctorate from the University of Warsaw with a thesis based on the papers he had written at Bydgoszcz.

Since no one in Poland was able to gauge the importance of his statistical work (he was “sui generis”, as he later described his situation), the Polish authorities provided an opportunity for Neyman to establish his credibility through publication in British journals. For this purpose they gave him a fellowship to work with Karl Pearson in London. He did publish three papers in *Biometrika* (based in part on his earlier work), but scientifically the academic year (1925–1926) spent in Pearson’s laboratory was a disappointment. He found the work of the laboratory old-fashioned and Pearson himself surprisingly ignorant of modern mathematics. (The fact that Pearson did not understand the difference between independence and lack of correlation led to a misunderstanding that nearly terminated Neyman’s stay at the laboratory.) So when, with the help of Pearson and Sierpiński, he received a Rockefeller fellowship that made it possible for him to stay in the West for another year, he decided to spend it in Paris rather than in London.

In Paris, Neyman attended the lectures of Lebesgue and a seminar of Jacques Hadamard. “I felt that this was real mathematics worth studying”, he wrote later, “and, were it not for Egon Pearson [Karl’s son], I would have probably drifted to my earlier passion for sets, measure and integration, and returned to Poland as a faithful member of the Warsaw school and a steady contributor to *Fundamenta Mathematicae”*.

**The Neyman-Pearson Theory** . What pulled Neyman back into statistics was a letter he received in the fall of 1925 from Egon Pearson, with whom he had had little contact in London. Egon had begun to question the rationale underlying some of the current work in statistics, and the letter outlined his concerns. A correspondence developed and, reinforced by occasional joint holidays, continued even after the end of the Rockefeller year, when Neyman returned to a hectic and difficult life in Warsaw. He again took up his lectures at the university (as docent after his habilitation in 1928). At the Central College of Agriculture, and at the University of Kraków. In addition, he founded a small statistical laboratory at the Nencki Institute for Experimental Biology. To supplement his meager academic income, and to provide financial support for the students and young co-workers in his laboratory, Neyman took on a variety of consulting jobs. These involved different areas of application, with the majority coming from agriculture and from the Institute for Social Problems, the latter work being concerned with Polish census data.

Neyman felt harassed, and his financial situation was always precarious. The bright spot in this difficult period was his work with the younger Pearson. Trying to find a unifying, logical basis that would lead systematically to the various statistical tests that had been proposed by William S. Gossett (also “Student”) and Ronald A. Fisher was a “big problem” of the kind for which he had hoped since his student days with Bernstein.

In 1933 Karl Pearson retired from his chair at University College, London, and his position was divided between Fisher and Egon Pearson. The latter lost no time and, as soon as it became available in the spring of 1934, offered Neyman a temporary position in his laboratory. Neyman was enthusiastic. This would greatly facilitate their joint work and bring relief to his Warsaw difficulties.

The set of issues addressed in the joint work of Neyman and Pearson between 1926 and 1933 turned out indeed to be a “big problem”, and their treatment of it established a new paradigm that changed the statistical landscape. What concerned Pearson when he first approached Neyman in 1926 was the ad hoc nature of the small sample tests being studied by Fisher and “Student”. In his search for a general principle from which such tests could be derived, he had written to “Student”. In his reply “Student” had suggested that one would be inclined to reject a hypothesis under which the observed sample is very improbable “if there is an alternative hypothesis which will explain the occurrence of the sample with a more reasonable probability” (E.S. Pearson, in David, ed., 1966). This comment led Pearson to propose to Neyman the likelihood ratio criterion, in which the maximum likelihood of the observed sample under the alternatives under consideration is compared with its value under the hypothesis. During the next year Neyman and Pearson studied this and other approaches, and worked out likelihood ratio tests for some important examples. They published their results in 1928 in a fundamental two-part paper, “On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference”. The paper contained many of the basic concepts of what was to become the Neyman-Pearson theory of hypothesis testing, such as the two types of error, the idea of power, and the distinction between, simple and composite hypotheses.

Although Pearson felt that the likelihood ratio provided the unified approach for which he had been looking, Neyman was not yet satisfied. It seemed to him that the likelihood principle itself was somewhat ad hoc and had no fully logical basis. However, in February 1930, he was able to write Pearson that he had found “a rigorous argument in favour of the likelihood method”. His new approach consisted of maximizing the power of the test, subject to the condition that under the hypothesis (assumed to be simple), the rejection probability has a preassigned value (the level of the test). He reassured Pearson that in all cases he had examined so far, this logically convincing test coincided with the likelihood ratio test. A month later Neyman announced to Pearson that he now had a general solution to the problem of testing a simple hypothesis against a simple alternative. The result in question is the fundamental lemma, which plays such a crucial role in the Neyman-Pearson theory.

The next step was to realize that in the case of more than one alternative, there might exist a uniformly most powerful test that would simultaneously maximize the power for all of them. If such a test exists. Neyman found, it coincides with the likelihood ratio, test, but in the contrary case—alas—the likelihood ration test may be biased. These results, together with many examples and elaborations, were published in 1933 under the title “On the Problem of the Most Efficient Tests of Statistical Hypotheses”, While in the 1928 paper the initiative and insights had been those of Pearson, who had had to explain to Neyman what he was doing, the situation was now reversed, with the leadership having passed to Neyman, leaving Pearson a somewhat reluctant follower.

The 1933 work is the fundamental paper in the theory of hypothesis testing. It established a framework for this theory and stated the problem of finding the best test as a clearly formulated, logically convincing mathematical problem that one can then proceed to solve. Its importance transcends the theory of hypothesis testing since it also provided the inspiration for Abraham Wald’s later, much more general statistical decision theory.

**Survey Sampling and Confidence Estimation** . In the following year Neyman published another landmark paper. An elaboration of work on survey sampling he had done earlier for the Warsaw Institute for Social Problems, it was directed toward bringing clarity into a somewhat muddled discussion about the relative merits of two different sampling methods. His treatment, described by Fisher as “luminous,” introduced many important concepts and results, and may be said to have initiated the modern theory of survey sampling.

The year 1935 brought two noteworthy events. The first was Neyman’s appointment to a permanent position as reader (associate professor) in Pearson’s department. Although at the time he was still hoping eventually to return to Poland, he in fact never did, except for brief visits. The second event was the presentation at a meeting of the Royal Statistical Society of an important paper on agricultural experimentation in which he raised some questions concerning Fisher’s Latin Square design. This caused a break in their hitherto friendly relationship and was the beginning of lifelong disputes.

Neyman remained in England for four years (1934 to 1938). During this time he continued his collaboration with Egon Pearson on the theory and applications of optimal tests, efforts that also included contributions from graduate and postdoctoral students. To facilitate publication and to emphasize the unified point of view underlying this work, Neyman and Pearson set up a series, Statistical Research Memoirs, published by University College and restricted to work done in the department of statistics. A first volume appeared in 1936, and a second in 1938.

Another central problem occupying Neyman during his London years was the theory of estimation: not point estimation, in which a parameter is estimated by a unique number but estimation by means of an interval or more general set in which the unknown parameter can be said to lie with specified confidence (probability), Such confidence sets are easily obtained under the Bayesian assumption that the parameter is itself random with a known probability distribution, but Neyman’s aim was to dispense with such an assumption, which he considered arbitrary and unwarranted.

Neyman published brief accounts of his solution to this problem in 1934 and 1935, and the theory in full generality in 1937, in “Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability.”

Neyman’s approach was based on the idea of obtaining confidence sets *S(X)* for a parameter θ from acceptance regions for the hypotheses that θ = θ_{0} by taking for *S(X)* the set of all parameter values θ_{0} that would be accepted at the given level. This formulation established an equivalence between confidence sets and families of tests, and enabled him to transfer in entirety the test theory of the 1933 paper—lock, stock, and barrel—to the theory of estimation. (Unbeknown to Neyman, the idea of obtaining confidence sets by inverting an acceptance rule had already been used in special cases by Pierre-Simon de Laplace—in a large-sample binomial setting—and by Harold Hotelling.)

In his paper on survey sampling, Neyman had referred to the relationship of his confidence intervals to Fisher’s fiducial limits, which appeared to give the same results although derived from a somewhat different point of view. In the discussion of the paper, Fisher welcomed Neyman as an ally in the effort to free statistics from unwarranted Bayesian assumptions, but then proceeded to indicate the disadvantages he saw in Neyman’s formulation. The debate between the two men over their respective approaches continued for many years, usually in less friendly terms; it is reviewed by Neyman in “Silver Jubilee of My Dispute with Fisher” (*Journal of the Operations Research Society of Japan*, **3** [1961], 145–154).

**Statistical Philosophy** . During the period of his work with Pearson, Neyman’s attitude toward probability and hypothesis testing gradually underwent a radical change. In 1926 he tended to favor a Bayesian approach in the belief that any theory would have to involve statements about the probabilities of various alternative hypotheses, and hence an assumption of prior probabilities. In the face of Pearson’s (and perhaps also Fisher’s) strongly anti-Bayesian position, he became less certain, and in his papers of the late 1920’s (both alone and with Pearson), he presented Bayesian and non-Bayesian approaches side by side. A decisive influence was Richard von Mises’s book *Wahrscheinlichkeit, Statistik und Wahrheit* (1928), about which he later wrote (*A Selection of Early Statistical Papers of J. Neyman*, 1967; author’s note) that it “confirmed him as a radical “frequentist’ intent on probability as a mathematical idealization of relative frequency.” He remained an avowed frequentist and opposed any subjective approach to science for the rest of his life.

A second basic aspect of Neyman’s work from the 1930’s on is a point of view that he formulated clearly in the closing pages of his presentation at the 1937 Geneva conference, “L’estimation statistique traitée comme un probléme classique de probabilité” (*Actualités scientifiques et industrielles*, no. 739, 25–57). He states that his approach is based on the concept of “comportement inductif,” or inductive behavior, instead of on inductive reasoning. That is, statistics is to use experience not to extract “beliefs” but as a guide to appropriate action.

In other writings (for example, in *Review of the International Statistical Institute*, **25** [1957], 7–22). Neyman acknowledges that a very similar point of view was advocated by Carl F. Gauss and Laplace. It is of course also that of Wald’s later general statistical decision theory. This view was strongly attacked by Fisher (for example, in *Journal of the Royal Statistical Society*, **B17** [1955], 69–78), who maintained that decision making has no role in scientific inference, and that his fiducial argument provides exactly the mechanism required for scientific inference.

**Move to the United States** . By 1937 Neyman’s work was becoming known not only in England and Poland but also in other parts of Europe and in the United States. He gave an invited talk about the theory of estimation at the International Congress of Probability held in 1937 at Geneva, and in the spring of 1937 he spent six weeks in the United States on a lecture tour organized by S.S. Wilks. The visit included a week at the graduate school of the Department of Agriculture in Washington, arranged by W.E. Deming. There he gave three lectures and six conferences on the relevance of probability theory to statistics, and on his work in hypothesis testing, estimation, sampling, and agricultural experimentation as illustrations of this approach. These *Lectures and Conferences on Mathematical Statistics*, which provided a coherent statement of the new paradigm he had developed and exhibited its successful application to a number of substantive problems, were a tremendous success. A mimeographed version appeared in 1938 and was soon sold out. Neyman published an augmented second edition in 1952.

After his return from the United States, Neyman debated whether to remain in England, where he had a permanent position but little prospect of promotion and independence, or to return to Poland. Then, in the fall of 1937, he received an unexpected letter from G.C. Evans, chairman of the department of mathematics at Berkeley, offering him a position in his department. Neyman hesitated for some time. California and its university were completely unknown quantities, while the situation in England—although not ideal—was reasonably satisfactory and offered stability. An attractive aspect of the Berkeley offer was the nonexistence there of any systematic program in statistics, so that he would be free to follow his own ideas. What finally tipped the balance in favor of Berkeley was the threat of war in Europe. Thus in April 1938 he decided to accept the Berkeley offer and immigrate to America, with his wife Olga (from whom he later separated) and his two-year-old son, Michael. He had just turned forty-four and he would remain in Berkeley for the rest of his long life.

**The Berkeley Department of Statistics** . Neyman’s top priority after his arrival in Berkeley was the development of a statistics program, that is, a systematic set of courses and a faculty to teach them. He quickly organized a number of core courses and began to train some graduate students and one temporary instructor in his own approach to statistics. Administratively, he set up a statistical laboratory as a semiautonomous unit within the mathematics department. However, America’s entry into World War II in 1941 soon put all further academic development on hold. Neyman took on war work, and for the next years this became the laboratory’s central and all-consuming activity.

The building of a faculty began in earnest after the war, and by 1956 Neyman had established a permanent staff of twelve members, many his own students but also including three senior appointments from outside (Michel Loève, Miriam Scheffé, and David Blackwell). Development of a substantial faculty, with the attendant problems of space, clerical staff, summer support, and so on, represented a major, sustained administrative effort. A crucial issue in the growth of the program concerned the course offerings in basic statistics by other departments, Although these involved major vested interests, Neyman gradually concentrated the teaching of statistics within his program, at least at the lower division level. This was an important achievement both in establishing the identity of the program and in obtaining the student base, which alone could justify the ongoing expansion of the faculty. In his negotiations with the administration, Neyman was strengthened by the growing international reputation of his laboratory and by the increasing postwar importance of the field of statistics itself.

An important factor in the laboratory’s reputation was the series of international symposia on math ematical statistics and probability that Neyman organized at five-year intervals between 1945 and 1970, and the subsequent publication of their proceedings. The first symposium was held in August 1945 to celebrate the end of the war and “the return to theoretical research” after years of war work. The meeting, although rather modest compared with the later symposia, was such a success that Neyman soon began to plan another one for 1950. In later years the symposia grew in size, scope, and importance, and did much to establish Berkeley as a major statistical center.

The spectacular growth Neyman achieved for his group required a constant struggle with various administrative authorities, including those of the mathematics department. To decrease the number of obstacles, and also to provide greater visibility for the statistics program, Neyman soon after his arrival in Berkeley began a long effort to obtain independent status for his group as a department of statistics. A separate department finally became a reality in 1955, with Neyman as its chair. He resigned the chairmanship the following year (but retained the directorship of the laboratory to the end of his life). He felt, he wrote in his letter of resignation, that “the transformation of the old Statistical Laboratory into a Department of Statistics closed a period of development . . . and opened a new phase.” In these circumstances, he stated, “it is only natural to have a new and younger man take over.”

There was perhaps another reason. Much of Neyman’s energy during the nearly twenty years he had been at Berkeley had gone into administration. His efforts had been enormously successful: a first-rate department, the symposia, a large number of grants providing summer support for faculty and students. It was a great accomplishment and his personal creation, but now it was time to get back more fully into research.

**Applied Statistics** . Neyman’s research in Berkeley was largely motivated by his consulting work, one of the purposes for which the university had appointed him and through which he made himself useful to the campus at large. Problems in astronomy, for example, led to the interesting insight (1948, with Scott) that maximum likelihood estimates may cease to be consistent if the number of nuisance parameters tends to infinity with increasing sample size. Also, to simplify maximum likelihood computations, which in applications frequently became very cumbersome, he developed linearized, asymptotically equivalent methods—his BAN (best asymptotically normal) estimates (1949)—that have proved enormously useful.

Neyman’s major research efforts at Berkeley were devoted to several large-scale applied projects. These included questions regarding competition of species (with T. Park), accident proneness (with G. Bates), the distribution of galaxies and the expansion of the universe (with C.D. Shane and particularly Elizabeth Scott, who became a steady collaborator and close companion), the effectiveness of cloud seeding, and a model for carcinogenesis. Of these, perhaps the most important was the work in astronomy, where the introduction of the Neyman-Scott clustering model brought new methods into the field.

Neyman’s applicational work, although it over many different areas, exhibits certain common features, which he made explicit in some of his writings and which combine into a philosophy for applied statistics. The following are some of the principal aspects.

1. The studies are indeterministic. Neyman has pointed out that the distinction between deterministic and indeterministic studies lies not so much in the nature of the phenomena as in the treatment accorded to them (“Indeterminism in Science and New Demands on Statisticians,” in *Journal of the American Statistical Association*, **55** [1960], 625–639). In fact, many subjects that traditionally were treated as deterministic are now being viewed stochastically. Neyman himself has contributed to this change in several areas.

2. An indeterministic study of a scientific phenomenon involves the construction of a stochastic model. In this connection Neyman introduced the important distinction between models that are interpolatory devices and those that embody genuine explanatory theories. The latter he describes as “a set of reasonable assumptions regarding the mechanism of the phenomena studied,” while the former “by contrast consist of the selection of a relatively ad hoc family of functions, not deduced from underlying assumptions, and indexed by a set of parameters” (“Stochastic Models and Their Application to Social Phenomena,” presented at a joint session of the Institute of Mathematical Statistics, the American Statistical Association, and the American Sociological Society, September 1956; written with W. Kruskal). The distinction is discussed earlier, and again later in Neyman’s papers (*Annals of Mathematical Statistics*, **10** [1939], 372–373; and *Reliability and Biometry*, [Philadelphia, 1974], 183–201).

Most actual modeling, Neyman points out, is in termediate between these two extremes, often exhibiting features of both kinds. Related is the realization that investigators will tend to use as building blocks models that, “partly through experience and partly through imagination, appear to us familiar and, therefore, simple” (“Stochastic Models of Population Dynamics”).

3. To develop a “genuine explanatory Theory” requires substantial knowledge of the scientific background of the problem. When the investigation concerns a branch of science with which the statistician is unfamiliar, this may require a considerable amount of work. For his collaboration with Scott in astronomy. Neyman studied the astrophysical literature, joined the American Astronomical Society, and became a member of the Commission on Galaxies of the International Astronomical Union. When he developed an interest in carcinogenesis, he spent three months at the National Institutes of Health to learn more about the biological background of the problem.

An avenue for learning about the state of the art in a field and bringing together diverse points of view that Neyman enjoyed and repeatedly used was to arrange a conference. Two of these (on weather modification in 1965 and on molecular biology in 1970) became parts of the then-current symposia. In addition, in 1961, jointly with Scott, he arranged a conference on the instability of systems of galaxies, and in July 1981, with Lucien Le Cam and on very short notice, an interdisciplinary cancer conference.

**Epilogue** . A month after the cancer conference. Neyman died of heart failure at age eighty-seven. He had been in reasonable health until two weeks earlier, and on the day before his death was still working in the hospital, on a book on weather modification.

Neyman is recognized as one of the founders of the modern theory of statistics whose work on hypothesis testing, confidence intervals, and survey sampling has revolutionized both theory and practice. His enormous influence on the development of statistics is further greatly enhanced through the large number of his Ph.D. students.

His achievements were recognized by honorary degrees from the universities of Chicago, California, Stockholm, and Warsaw, and from the Indian Statistical Institute. He was elected to the United States National Academy of Sciences and to foreign membership in the Royal Society, the Royal Swedish Academy, and the Polish National Academy. In addition he received many awards, including the United States National Medal of Science and the Guy Medal in Gold of the Royal Statistical Society.

Neyman was completely and enthusiastically dedicated to his work, which filled his life; there was not time for hobbies. Work, however, included not only research and teaching but also social aspects, such as traveling to meetings and organizing conferences. Pleasing his guests was an avocation; his hospitality had an international reputation. In his laboratory he created a family atmosphere that included students, colleagues, and visitors, with himself as paterfamilias.

As an administrator Neyman was indomitable. He would not take no for an answer, and was quite capable of resorting to unilateral actions. He firmly believed in the righteousness of his causes and found it difficult to understand how a reasonable person could disagree with him. At the same time, he had great charm that often was hard to resist.

The characteristic that perhaps remains most in mind is his generosity: furthering the careers of his students, giving credit and doing more than his share in collaboration, and extending his help (including financial assistance out of his own pocket) to anyone who needed it.

## BIBLIOGRAPHY

I. Original Works. A complete bibliography of Neyman’s work is given at the end of David Kendall’s memoir, in *Biographical Memoirs of Fellows of the Royal Society* (see below). Some of the early papers are reprinted in *A Selection of Early Statistical Papers of J. Neyman* and *Joint Statistical Papers of J. Neyman and E.S. Pearson* (Berkeley, 1967). Neyman’s letters to E.S. Pearson from 1926 to 1933 (but not Pearson’s replies) are preserved in Pearson’s estate.

An overall impression of Neyman’s ideas and style can be gained from his *Lectures and Conferences on Mathematical Statistics and Probability*, 2nd, ed., rev. and enl. (Washington, D.C., 1952). The following partial list provides a more detailed view of his major paradigmatic papers: “On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference,” in *Biometrika*, **20A** (1928), 175–240, 263–294, written with E.S. Pearson: “On the Problem of the Most Efficient Tests of Statistical Hypotheses,” in *Philosophical Transactions of the Royal Society of London*, **A 231** (1933), 289–337, written with E.S. Pearson; “On the Two Different Aspects of the Representative Method,” in *Journal of the Royal Statistical Society*, **97** (1934), 558–625 (a Spanish version of this paper appeared in Estadistica, **17** [1959], 587–651); “Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability,” in *Philosophical Transactions of the Royal Society of London*, **A236** (1937), 333–380. Neyman’s other theoretical contributions include “‘Smooth’ Test for Goodness of Fit,” in *Skandinavisk aktuarietidskrift*, **20** (1937), 149–199; “On a New Class of ‘Contagious’ Distributions, Applicable in Entomology and Bacteriology,” in *Annals of Mathematical Statistics*, **10** (1939), 35–57; “Consistent Estimates Based on Partially Consistent Observations,” in *Econometrica*, **16** (1948), 1–32, written with E.L. Scott; “Contribution to the Theory of the Chi-Square Test,” in J. Neyman, ed., *Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability* (Berkeley, 1949); “Optimal Asymptotic Tests of Composite Statistical Hypotheses,” in U. Granander, ed., *Probability and Statistics* (Uppsala, Sweden, 1959), 213–234; “Outlier Proneness of Phenomena and of Related Distributions,” in J.S. Rustagi, ed., *Optimizing Methods in Statistics* (New York and London, 1971), 413–430, written with E.L. Scott.

Neyman’s position regarding the role of statistics in science can be obtained from the following more philosophical and sometimes autobiographical articles: “Foundation of the General Theory of Statistical Estimation, in *Actualités Scientifiques et industrielles*, no. 1146 (1951), 83–95; “The Problem of Inductive Inference,” in *Communications in Pure and Applied Mathematics*, **8** (1955), 13–45; “‘Inductive Behavior’ as a Basic Concept of Philosophy of Science,” in *Review of the International Statistical Institute*, **25** (1957), 7–22; *“Stochastic Models of Population Dynamics,” in Science* (New York), **130** (1959), 303–308, written with E.L. Scott; “A Glance at Some of My Personal Experiences in the Process of Research,” in T. Dalenius, G. Karlsson, and S. Malmquist, eds., *Scientists at Work* (Uppsala, Sweden, 1970), 148–164; and “Frequentist Probability and Frequentist Statistics,” in Synthèse, **36** (1977), 97–131.

II. Secondary Literature. The most important source for Neyman’s life and personality is Constance Reid, *Nevman—from Life* (New York, 1982), which is based on Neyman’s own recollections (obtained during weekly meetings over a period of more than a year) and those of his colleagues and former students, and on many original documents. A useful account of his collaboration with E.S. Pearson was written by Pearson for the Neyman festschrift. F.N. David, ed., *Research Papers in Statistics* (New York, 1966). Additional accounts of his life and work are provided by the following; D.G. Kendall, M.S. Bartlett, and T.L. Page, “Jerzy Neyman, 1894–1981,” in *Biographical Memoirs of Fellows of the Royal Society*, **28** (1982), 379–412; L. Le Cam and E.L. Lehmann, “J. Neyman—on the Occasion of his 80-th Birthday,” in *Annals of Statistics*, **2** (1974), vii-xiii; E.L. Lehmann and Constance Reid, “In Memoriam—Jerzy Neyman, 1894–1981,” in American Statistician, **36** (1982) 161–162; and E.L. Scott, “Neyman, Jerzy,” in *Encyclopedia of Statistical Sciences*, **VI** (1985) 215–223.

E. L. Lehmann

# Jerzy Neyman

# Jerzy Neyman

Jerzy Neyman (1894-1981) was a scholar, teacher, and pioneer of statistical mathematics and probability. He helped establish the field of statistical mathematics through the innovative Neyman-Pearson theory and by being a tireless advocate for its legitimacy.

Neyman was born on April 16, 1894, in Bendery, Russia. He was the second of four children of Czeslaw Splawa-Neyman and Kazimiera Lutoslawaska, who were Polish and Roman Catholics. Neyman's father was a judge, and the family frequently moved about Russia as required by his father's occupation. Neyman did not begin his formal education until he was ten, when he enrolled in school in Simferopol, located in Crimea. Although he lagged behind his classmates in Russian history and geography, young Neyman displayed advanced knowledge of Polish, Russian, French, German, and Ukranian, among other subjects.

In 1906, Neyman's father died suddenly of a heart attack. To secure an income, Neyman's mother moved the family to Kharkov in the Ukraine, where she was employed as the manager of an estate belonging to her late husband's relatives. Enrolling in the local school, Neyman proved a superior student and graduated in 1912.

## Moved to Poland

Neyman entered the University of Kharkov (later Maxim Gorki University). Although he intended to study mathematics, he was temporarily drawn to physics by the groundbreaking work of Albert Einstein and Marie Curie. However, when Neyman was introduced to the advancements in calculus made by French mathematician Henri-Leon Lebesgue, he refocused his studies on mathematics and continued in the field for the remainder of his life. Although he did not meet Lebesgue until 1926, Neyman considered him his mentor. For his undergraduate thesis he submitted a paper entitled "Integral of Lebesgue," which was awarded a gold medal. He also studied mathematics and probability under S. N. Berstein. Graduating in September 1917, Neyman enrolled in the graduate school in mathematics at the University of Kharkov and also became a lecturer in mathematics at the Kharkov Institute of Technology.

The next four years were eventful for Neyman. It was a turbulent period politically in Russia, with the Communist Revolution and subsequent turmoil. During the Russian-Polish conflict, Neyman was imprisoned for a time as an enemy of the state due to his Polish heritage. He also was arrested for selling matches on the black market. On May 4, 1920, Neyman married Olga Solodovnikova, a Russian of the Orthodox faith.

Although official academic degrees were no longer bestowed under Soviet rule, examinations were still given as evidence of educational achievements. In the fall of 1920, Neyman passed the examinations for his master's degree at the University of Kharkov and remained at the university to teach a variety of mathematical courses. However, by the end of his first year of teaching, Neyman received word that he was about to be arrested again. As a result, he moved with his wife, mother, and grandmother out of Russia to Poland.

## Early Work in Mathematics

In Poland, he accepted a position as the senior statistical assistant for the National Agricultural Institute in Bydgoszcz. During the two years he spent there, Neyman began working on numerous papers that applied mathematical probability to agricultural problems.

In 1923 Neyman accepted an offer to direct the Biometric Laboratory of the Nencki Institute for Experimental Biology in Warsaw and began lecturing at the Central College of Agriculture in Warsaw. He also continued his advanced studies and graduated with his doctoral degree in mathematics from the University of Warsaw in 1924. Continuing his interest in statistical probability, Neyman submitted his dissertation in two papers that addressed issues of probability related to agricultural experimentation. Written in Polish and summarized in French, the papers were titled "On the Applications of the Theory of Probability to Agricultural Experiments" and "Memoir on the Application of Mathematical Statistics on Resolving Some Agricultural Problems." The papers provided a careful analysis of problems in estimation, including a preliminary discussion of "true value." However, because Neyman was at that time unaware of groundbreaking statistical work being done in England, the impact of his work was limited.

Having received his Ph.D., Neyman began teaching mathematical and statistical courses at the University of Warsaw, the Central College of Agriculture, and the University of Kharkov. In the fall of 1925, with the help of a postdoctoral fellowship from the University of Warsaw, Neyman traveled to London to study at the Biometric Laboratory at University College. The laboratory was run by Karl Pearson, author of the influential mathematical work *Grammar of Science* and commonly considered the founder of modern statistics. During his year in London, Neyman worked with those on the leading edge of mathematics, including William S. Gosset.

## The Neyman-Pearson Theory

Neyman's most influential relationship in London was with Karl Pearson's son, Egon Pearson, with whom he would collaborate in the study of hypothesis testing, leading to significant advancements in modern statistical methodology. The two decided to continue their investigation via letters and occasional meetings. What resulted from their combined work between 1928 and 1933 became known as the Neyman-Pearson theory, or the Neyman-Pearson fundamental lemma. Their first joint paper was published in 1928. It was followed by a series of ten published papers that culminated in 1933 with the publication of "On the Problem of the Most Efficient Tests of Statistical Hypotheses." According to L. E. Lehmann in "The Neyman-Pearson Theory After Fifty Years," his contribution to the *Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer* (1985), "Despite the fact that these ideas had their forerunners in the work of [English mathematician R. A.] Fisher, the Neyman-Pearson paradigm formulated for the first time a clear program and provided a completely novel approach to hypothesis testing, the first 'exact' small-sample theory of its kind."

The goal of the Neyman-Pearson theory is to draw conclusions regarding a hypothesis even though there exists the possibility of error. Neyman and Pearson distinguished two error types. A Type I error occurs when a true hypothesis is deemed false (false negatives), and a Type II error occurs when a false hypothesis is deemed true (false positives). When a decision must be made under uncertain conditions, Neyman's methodology provided a means to lessen the occurrence of error, even when the outcome was based solely on chance, by establishing what Neyman referred to as "confidence intervals."

## Economic Struggles

In 1926 Neyman continued his postdoctoral studies, spending the academic year in Paris with the support of a Rockefeller Fellowship. The next year he returned to Poland and assumed his position as faculty docent at the University of Warsaw. He also worked diligently to establish a small biometric laboratory at the Nencki Institute for Experimental Biology. Although his fame as a mathematician and statistician eventually placed him among the elite of the academic world, he was never offered a full professorship in Poland, and his economic situation in Poland proved precarious. In "The Neyman-Pearson Story: 1926-1934," an article in *Research Papers in Statistics* (1966), Egon Pearson quotes Neyman from a personal letter, dated June 23, 1932: "I simply cannot work; the crisis and the struggle for existence takes all my time and energy. I am not sure that next year I shall not be obliged to take some job, I do not know where—in trade, perhaps, selling coal or handkerchiefs."

At the end of 1933, Pearson invited Neyman to join him on the faculty of the University College in London, and Neyman accepted. At first he was a visiting professor, but in 1935 he was promoted to reader. In 1936 he was given a full professorship and put in charge of the university's statistical laboratory. During his tenure at University College, Neyman wrote two significant papers. One, published in 1934, laid the foundation for the sampling techniques that subsequently influenced the development of modern day public opinion polling. The other, published in 1937, expounded on his theory of confidence intervals. Neyman applied his statistical probability methodology, using randomized testing, to such practical areas as the spread of disease during epidemics, agricultural problems, and issues in chemistry, biology, physics, and medicine.

## Years at Berkeley

After a successful speaking tour of the United States in 1937, Neyman the following year accepted an offer from the University of California at Berkeley to join its faculty as a professor of statistical mathematics and to start a statistical laboratory. Neyman remained associated with the University of California for the remainder of his life. Although he was eager to establish his program at the university, World War II interrupted his plans, and by March 1942, Neyman had turned his attention to military research, namely bomb sights and targeting accuracy and patterns. In 1944, Neyman became a citizen of the United States. In 1950 he and wife, with whom he had one child, separated. They never legally divorced and lived within several miles of each other.

Once his attention was returned to the development of statistical studies at the University of California and its Berkeley Statistical Laboratory, Neyman methodically developed his work. Known as a generous and personable man, Neyman was steadfast in creating an intellectually superior program in mathematical statistics. In 1945 he established the Berkeley Symposia in Mathematical Statistics and Probability, which drew the best statistical minds in the world as speakers. He also diligently pressed University officials for recognition, funding, and resources for his work. In 1954, he succeeded in establishing the Department of Statistics as a separate program, and he was named as chair of the new department. None of his publications, during his tenure at Berkeley, had the impact of his previous published work. Yet he made an indelible mark on the field of statistics and probability as mentor and teacher to 39 Ph.D. students, several of whom became leading statisticians at Berkeley, including Erich Lehmann, Joseph Hodges, and Elizabeth Scott. Neyman retired from teaching at Berkeley in 1961 but remained as director of the Statistical Laboratory.

Neyman was highly influential in the development of statistical mathematics as both a scholar of original thought and as an ambassador for the field of study. His personality won him many friends and inspired him to take some difficult stands on issues outside the field of mathematics. After World War II, when the University of California required all faculty members to sign loyalty oaths, stating that they were not involved in any activities to overthrow the U.S. government, Neyman, who signed the oath, nonetheless supported those who refused to sign it. In the 1960s he became involved in the opposition to American involvement in the war in Vietnam.

For his numerous and important contributions, Neyman was awarded the Cleveland Prize of the American Association for the Advancement of Science in 1958 and the Samuel S. Wilks Medal by the American Statistical Association in 1964. He refused to attend the 1964 medal ceremony because it was held at an army base. In 1968, he was given the National Medal of Science. He was also the recipient of honorary degrees from the University of Chicago (1953), the University of California at Berkeley (1963), the University of Stockholm (1964), and the University of Warsaw (1974). Neyman remained active until the end of his life. He died of a heart attack on August 5, 1981, in Oakland, California.

## Books

*American Men and Women of Science,* Jacques Cattell Press/R.R. Bowker Co., 1972.

*American National Biography,* Volume 16, edited by John A. Garraty and Mark C. Carnes, Oxford University Press, 1999.

*McGraw-Hill Modern Scientists and Engineers,* edited by Jay E. Greene, McGraw-Hill, 1980.

*Proceedings of the Berkeley Conference in Honor of Jerzy Newman and Jack Kiefer,* Volume 1, edited by Lucien Le Cam and Richard A. Olshen, Wadsworth, 1985.

*Research Papers in Statistics,* edited by F.N. David, John Wiley and Sons, 1966.

## Online

"Jerzy Neyman," *Contemporary Authors Online,*http://www.galenet.com (January 18, 2001).

"Jerzy Neyman," *The Scribner Encyclopedia of American Lives, Volume 1: 1981-1985,*http://www.galenet.com (January 18, 2001). □

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