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.
Related Links
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Neyman.html
