Allan Birnbaum
Encyclopedia
Allan Birnbaum was an American statistician
who contributed to statistical inference
, foundations of statistics, statistical genetics
, statistical psychology, and history of statistics.
Birnbaum was born in San Francisco. His parents were Russian-born Orthodox Jews. He studied mathematics at the University of California
, doing a premedical programme at the same time. After taking a bachelor's degree in mathematics in 1945, he spent two years doing graduate courses in science, mathematics and philosophy, planning perhaps a career in the philosophy of science. One of his philosophy teachers, Hans Reichenbach
, suggested he combine philosophy with science.
He went to Columbia University
to do a PhD with Abraham Wald
but, when Wald died in a plane crash, Birnbaum asked Erich Leo Lehmann
, who was visiting Columbia to take him on. Birnbaum's thesis and his early work was very much in the spirit of Lehmann's classic text Testing Statistical Hypotheses.
Birnbaum stayed at Columbia until 1959 when he moved to the Courant Institute of Mathematical Sciences
, becoming a full Professor of Statistics in 1963. He travelled a good deal and liked Britain especially. In 1975 he accepted a post at the City University, London
, and worked with The Open University on their course M341 (with Adrian Smith
). He had problems relating to his wife and child, and he killed himself in 1976.
The article in the Leading Personalities volume opens with the declaration, "Allan Birnbaum was one of the most profound thinkers in the field of foundations of statistics." The assessment is based on Birnbaum's 1962 article and the publications surrounding it. Birnbaum's argument for the likelihood principle
generated great controversy; it implied, amongst other things, a repudiation of the approach of Wald and Lehmann, that Birnbaum had followed in his own research. Leonard Jimmie Savage
opened the discussion by saying
Although Birnbaum made other contributions, none compared with this for impact or continuing resonance.
For information about Birnbaum's correspondence with R. A. Fisher (and a copy of one letter) see
Statistician
A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. The core of that work is to measure, interpret, and describe the world and human activity patterns within it...
who contributed to statistical inference
Statistical inference
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...
, foundations of statistics, statistical genetics
Population genetics
Population genetics is the study of allele frequency distribution and change under the influence of the four main evolutionary processes: natural selection, genetic drift, mutation and gene flow. It also takes into account the factors of recombination, population subdivision and population...
, statistical psychology, and history of statistics.
Birnbaum was born in San Francisco. His parents were Russian-born Orthodox Jews. He studied mathematics at the University of California
University of California
The University of California is a public university system in the U.S. state of California. Under the California Master Plan for Higher Education, the University of California is a part of the state's three-tier public higher education system, which also includes the California State University...
, doing a premedical programme at the same time. After taking a bachelor's degree in mathematics in 1945, he spent two years doing graduate courses in science, mathematics and philosophy, planning perhaps a career in the philosophy of science. One of his philosophy teachers, Hans Reichenbach
Hans Reichenbach
Hans Reichenbach was a leading philosopher of science, educator and proponent of logical empiricism...
, suggested he combine philosophy with science.
He went to Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
to do a PhD with Abraham Wald
Abraham Wald
- See also :* Sequential probability ratio test * Wald distribution* Wald–Wolfowitz runs test...
but, when Wald died in a plane crash, Birnbaum asked Erich Leo Lehmann
Erich Leo Lehmann
Erich Leo Lehmann was an American statistician, who contributed to statistical and nonparametric hypothesis testing...
, who was visiting Columbia to take him on. Birnbaum's thesis and his early work was very much in the spirit of Lehmann's classic text Testing Statistical Hypotheses.
Birnbaum stayed at Columbia until 1959 when he moved to the Courant Institute of Mathematical Sciences
Courant Institute of Mathematical Sciences
The Courant Institute of Mathematical Sciences is an independent division of New York University under the Faculty of Arts & Science that serves as a center for research and advanced training in computer science and mathematics...
, becoming a full Professor of Statistics in 1963. He travelled a good deal and liked Britain especially. In 1975 he accepted a post at the City University, London
City University, London
City University London , is a public research university located in London, United Kingdom. It was founded in 1894 as the Northampton Institute and became a university in 1966, when it adopted its present name....
, and worked with The Open University on their course M341 (with Adrian Smith
Adrian Smith (academic)
Sir Adrian Frederick Melhuish Smith FRS is a distinguished British statistician and formerly Principal of Queen Mary, University of London. He was previously at Imperial College, London where he was head of the Mathematics Department. He is a member of the governing body of the London Business...
). He had problems relating to his wife and child, and he killed himself in 1976.
The article in the Leading Personalities volume opens with the declaration, "Allan Birnbaum was one of the most profound thinkers in the field of foundations of statistics." The assessment is based on Birnbaum's 1962 article and the publications surrounding it. Birnbaum's argument for the likelihood principle
Likelihood principle
In statistics,the likelihood principle is a controversial principle of statistical inference which asserts that all of the information in a sample is contained in the likelihood function....
generated great controversy; it implied, amongst other things, a repudiation of the approach of Wald and Lehmann, that Birnbaum had followed in his own research. Leonard Jimmie Savage
Leonard Jimmie Savage
Leonard Jimmie Savage was an American mathematician and statistician. Nobel Prize-winning economist Milton Friedman said Savage was "one of the few people I have met whom I would unhesitatingly call a genius."...
opened the discussion by saying
Without any intent to speak with exaggeration or rhetorically, it seems to me that this is really a historic occasion. This paper is landmark in statistics because it seems to me improbable that many people will be able to read this paper or to have heard it tonight without coming away with considerable respect for the likelihood principle.
Although Birnbaum made other contributions, none compared with this for impact or continuing resonance.
Publications of Allan Birnbaum
41 papers are listed by Barnard and Godambe. The first appeared in 1953 and the last, posthumously, in 1977. The most celebrated is the 1962 paper on the likelihood principle. (With discussion.)External links
For Birnbaum’s PhD students seeFor information about Birnbaum's correspondence with R. A. Fisher (and a copy of one letter) see