Statisticians in History

Jerzy Neyman 

Jerzy  Neyman

by Chin Long Chiang, Professor in the Graduate School, University of California, Berkeley

Jerzy Neyman, one of the principal architects of modern statistics, was Director of the Statistical Laboratory, University of California, Berkeley. He was born on April 16, 1894, into a Polish family in Bendery, Russia, and died on August 5, 1981, in Berkeley, California, at the age of 87. With Neyman's passing, history closed a chapter on the early development of this important scientific field.

At the time of his birth, there was no Poland as a nation. "Poland proper" had been divided among Germany, Austria, and Russia. Neyman's father was a lawyer. When Neyman was twelve years old, his father died of a heart attack. His caring mother moved her family to Kharkov, where he attended school and college. Although he was born a Pole, Neyman spoke Russian almost as early as he spoke Polish. At an early age, he could also speak Ukrainian, German, French, and Latin fluently. Upon his graduation from high school, through his mother's arrangement, he joined a student group making a journey to see Europe outside Russia. Before entering the college in Kharkov, he decided to study mathematics instead of pursuing his father's profession. He received his mother's support and encouragement. "She had respect for intellectual activity," Neyman fondly recalled to Constance Reid in the late 1970s. (Reid published her book entitled Neyman From Life in 1982.) In 1921, after a Polish-Soviet peace treaty, Neyman was sent to Poland in a repatriation of prisoners of war program between the two countries. Neyman saw his fatherland Poland for the first time when he was 27 years old.

Neyman's interest in mathematics was reinforced when he studied with the Russian probabilist S. N. Bernstein at the University of Kharkov. When he read Henri Lebesgue's Lecons sur L'intégration et la Recherche des Functions Primitives, Neyman was fascinated by sets, measure, and integration. During his college days he had proved five theorems on the Lebesgue integral on his own. His article entitled "Sur une théoréme metrique concernant les ensembles fermés," published in 1923, was one of his early research papers in pure mathematics. His candidate thesis at the University of Kharkov (1916) was on the integral of Lebesque. In 1917, Neyman returned to the university for postgraduate study. In the following year he was a docent at the Institute of Technology, Kharkov. At the University of Warsaw, Neyman studied mathematics with Waclaw Sierpinski. He earned the Doctor of Philosophy degree from the University of Warsaw in 1924. The oral examination consisted of Rigorosum Major in mathematics and Rigorosum Minor in philosophy. No one knew more statistics than Neyman to examine him on the subject.

In the little spare time that he had during his student days, Neyman was heavily involved in teaching to earn a living. He also gave supplementary lectures for professors at the university and taught mathematics and statistics to college students.

Neyman first heard of Karl Pearson from reading Pearson's book Grammar of Science (1892). Apparently, he was influenced by Pearson's philosophical views as expressed in the book.

Neyman's contact with statistics occurred early in his academic career. It appears that he had studied applications of mathematical statistics with Bernstein at the University of Kharkov. But he learned most statistics through work on his own, especially in agricultural experimentation. He held a position of "senior statistical assistant" at the National Agricultural Institute in Bydgoszcz, Poland, in 1921, and he was a special lecturer at the Central College of Agriculture in Warsaw in 1922.

In the fall of 1925, Sierpinski and Kazimierz Bassalik, the director of the National Agricultural Institute, were awarded a Polish Government Fellow-ship for Neyman to study mathematical statistics with Karl Pearson in London. Neyman was well prepared in mathematics and in statistics. While in London, Neyman and a young man about his own age, Pearson's son Egon S. Pearson, became good friends.

During the academic year 1926-27, Neyman was on a Rockefeller fellowship to study pure mathematics in Paris. He attended lectures given by Emile Borel at the University of Paris and also lectures by Lebesgue and Jacques Hadamard at the College de France. In addition, he had some of his own notes read at these institutes. Quite possibly, the year of studying mathematics in Paris had prepared him well for his joint endeavor with Egon Pearson in the development of statistical theory in the years to come.

Neyman and Pearson's joint work formally started in the spring of 1927, when Pearson visited Neyman in Paris. While there are no records of what transpired during the ten days during which they worked together, they must have laid out plans for their future joint project. At the end of the 1926-27 academic year, Neyman went back to Poland, and in 1928 he became head of the Biometric Laboratory at the Nencki Institute of Warsaw. He carried out his joint
work with Pearson through correspondence between Warsaw and London. From 1928 to 1934, they published seven of their ten most important papers on the theory of testing statistical hypotheses.

In developing their theory, Neyman and Pearson recognized the need to include alternative hypotheses and they perceived the errors in testing hypotheses concerning unknown population values based on sample observations that are subject to variation. They called the error of rejecting a true hypothesis the first kind of error and the error of accepting a false hypothesis the second kind of error. They placed importance on the probability of rejecting a hypothesis when it is false. They called this probability the power of test. They proposed a term, "critical region" to denote a set of sample statistical values leading to the rejection of the hypothesis being tested. The "size" of a critical region is the probability of making the first kind of error, which they called the level of significance.

They called a hypothesis that completely specifies a probability distribution a simple hypothesis. A hypothesis that is not a simple hypothesis is a composite hypothesis. A hypothesis concerning the mean of a normal distribution with a known standard deviation, for example, is a simple hypothesis. The hypothesis is a composite hypothesis if the standard deviation is unknown.

It is now difficult for us to imagine how one could perform a statistical test without these concepts. But the Neyman- Pearson theory was a considerable departure from traditional hypothesis testing at the time. They were severely criticized for their new theory by the leading authorities of the field, especially by R. A. Fisher.

Neyman and Pearson used conceptual mathematics and logical reasoning to develop the theory of hypothesis testing. They emphasized "the importance of placing in a logical sequence the stages of reasoning in the solution of ...inference." In their initial papers (1928a) and (1928b), it seems that they were leading the reader, step by step, in their development of the theory. They relied on the concept of likelihood ratio in testing hypotheses concerning parameters in known probability distributions. And they elucidated their ideas further with specific examples and numerical computations.

After they had laid a solid mathematical foundation for their theory, they applied it to the problem of two samples (1930) and to the problem of k samples (1931). In one of their joint papers (1933) they used the likelihood ratio to establish an objective criterion for determining the best (in the sense of power of test) critical region for testing a simple hypothesis and a composite hypothesis. That was a high point of their accomplishment. The landscape of statistical hypothesis testing would no longer be the same.

In 1934, Neyman joined the faculty of E. S. Pearson's Department of Applied Statistics at the University College London. From 1934 to 1938, they published only three more joint papers on testing hypotheses, possibly because of Pearson's involvement in administrative responsibilities. Neyman, however, was still very productive during that period. From time to time, Neyman published papers on hypothesis testing on his own but most of the fundamental work was contained in his joint publications with Pearson.

When he was still in Poland, Neyman had developed the idea of confidence interval estimation. He even gave lectures on confidence interval estimation rather than hypothesis testing in his class at University College London in 1934. He published his work in 1937. At that time, many statisticians confused the confidence interval with the fiducial interval, a concept developed by Fisher. That confusion was soon dispelled by Fisher himself. Neyman clarified the difference between the two in his Lectures and Conferences (1938).

In addition to the theory of statistical inference, Neyman had made contributions to many other branches of statistics, such as the designs of agricultural experimentation (1923, 1925, 1935), the theory of sampling (1925, 1938, 1939), a class of "contagious" distributions (1939), and others. He even used the "storks bring babies" example to show how to reach a wrong conclusion by misusing a correlation between variables, the so-called spurious correlation (1938).
Neyman's work of applications of statistical methods in practical problems was very extensive. He considered practical problems as a source of inspiration for the theoretical statisticians.

There was an interesting feature in Neyman's approach to practical problems. He had the ability to visualize the phenomena behind the data and a model of the mechanism that creates the phenomena. He would express the model in mathematical terms to produce new probability distributions, or new stochastic models. Only then would he find appropriate statistical methods to analyze the data on hand.

In the spring of 1937 Neyman delivered a series of lectures on mathematical statistics an probability at the Graduate School in the U.S. Department of Agriculture in Washington, DC. That was the first time that the American statistical public had the opportunity to hear statistical theory from Neyman in person. The lecture notes were subsequently published in 1937, and revised and expanded in 1952, under the title Lectures and Conferences on Mathemat-ical Statistics and Probability. Among the reviews of the 1937 book, there was one written by William Feller, published in Zentralblatt, which reads in part as follows:

"The point of departure for the author is always actual practical problem and he never loses sight of the applications. At the same time his goal is always a truly rigorous mathematical theory. He appears to insist on absolute conceptual clarity and rigor, not only as a sound foundation, but also because it is really useful and necessary, particularly where the practical problem goes beyond the mathematical aspect..."

Feller's words would apply equally well to Neyman's other publications.

In 1938, Neyman accepted a mathematics professorship from the University of California at Berkeley. And he established the Statistical Laboratory, with himself as the director. That was the beginning of one of the preeminent statistical centers in the world. In 1955, Neyman established the Department of Statistics. He retained the title Director of the Statistical Laboratory.

Neyman was a very dynamic person, full of ideas and energy. Soon after the Statistical Laboratory was established and the teaching program was in good order, he began to plan a symposium of mathematical statistics and probability "to mark the end of the war and to stimulate the return to theoretical research." The symposium had the participation of leading authorities in theoretical probability, in mathematical statistics, and in applied fields. The Proceedings of the symposium, edited by Neyman, were published in 1949 to "stimulate research and foster cooperation between the experimenter and the statistician."

Success of the symposium prompted Neyman to plan a series of symposia, once every five years. The number of participants and the coverage grew from one symposium to the next. The Sixth Berkeley Symposium, held in three different periods in 1970 and 1971, was attended by 240 leading authors in 33 subject areas in theory of probability, in mathematical statistics, and in scientific fields with applications of statistics. The Proceedings, edited by LeCam, Neyman, and Scott, were published in 1972 in six volumes and 3397 pages-a gigantic undertaking.

These symposia supplemented the teaching programs and research academic activities normally carried out in universities and other academic institutions. They also had a great deal of influence on the attitude of theoretical statisticians and research scientists, making them recognize the need and the advantage of applications of statistics.
During the forty years that he was in Berkeley, Neyman had students come from all over the world to attend his lectures and to learn the proper way of conducting research. Neyman was a generous man. He helped students financially in any way he could. He recommended students for University scholarships and he secured federal grants for the support of students and faculty. At times, when he could not obtain the funds he needed to support students from any other sources, Neyman took the money out of his own pocket.

Neyman used to say "Statistics is the servant to all sciences." In many ways Neyman had expanded the domain and improved the quality of the service.

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