Allan Birnbaum
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Allan Birnbaum (May 27, 1923 – July 1, 1976) was an American
statistician A statistician is a person who works with Theory, theoretical or applied statistics. The profession exists in both the private sector, private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, a ...
who contributed to
statistical inference Statistical inference is the process of using data analysis to infer properties of an underlying probability distribution.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers properties of ...
, foundations of statistics,
statistical genetics Statistical genetics is a scientific field concerned with the development and application of statistical methods for drawing inferences from genetic data. The term is most commonly used in the context of human genetics. Research in statistical ge ...
, statistical psychology, and history of statistics.


Life and career

Birnbaum was born in
San Francisco San Francisco, officially the City and County of San Francisco, is a commercial, Financial District, San Francisco, financial, and Culture of San Francisco, cultural center of Northern California. With a population of 827,526 residents as of ...
. His parents were Russian-born Orthodox Jews. He studied mathematics at the
University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...
, 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 (; ; September 26, 1891 – April 9, 1953) was a leading philosopher of science, educator, and proponent of logical empiricism. He was influential in the areas of science, education, and of logical empiricism. He founded the ''G ...
, suggested he combine philosophy with science. He went to
Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...
to do a PhD with
Abraham Wald Abraham Wald (; ; , ;  – ) was a Hungarian and American mathematician and statistician who contributed to decision theory, geometry and econometrics, and founded the field of sequential analysis. One of his well-known statistical works was ...
but, when Wald died in a plane crash, Birnbaum asked
Erich Leo Lehmann Erich Leo Lehmann (20 November 1917 – 12 September 2009) was a German-born American statistician, who made a major contribution to nonparametric hypothesis testing. He is one of the eponyms of the Lehmann–Scheffé theorem and of the Hodges ...
, 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 The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU). Founded in 1935, it is named after Richard Courant, one of the founders of the Courant Institute ...
, 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 of London was a public university from 1966 to 2024 in London, England. It merged with St George's, University of London to form City St George's, University of London in August 2024. The names "City, University of London" and ...
, and worked with
The Open University The Open University (OU) is a Public university, public research university and the largest university in the United Kingdom by List of universities in the United Kingdom by enrolment, number of students. The majority of the OU's undergraduate ...
on their course M341 "Fundamentals of statistical inference" (with
Adrian Smith Adrian Smith may refer to: * Adrian Smith (basketball) (born 1936), American basketball player *Adrian Smith (architect) (born 1944), American architect *Sir Adrian Smith (statistician) (born 1946), English statistician and academic *Adrian Smith (m ...
). He took his life 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 In statistics, the likelihood principle is the proposition that, given a statistical model, all the evidence in a sample relevant to model parameters is contained in the likelihood function. A likelihood function arises from a probability densit ...
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 (born Leonard Ogashevitz; 1917 – 1971) was an American mathematician and statistician. Economist Milton Friedman said Savage was "one of the few people I have met whom I would unhesitatingly call a genius." Education and ...
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.)''


Discussions

* * * – originally published in ''Encyclopedia of Statistical Science''.


See also

* CLs method (particle physics)#Allan Birnbaum


External links

For Birnbaum's PhD students see For information about Birnbaum's correspondence with R. A. Fisher (and a copy of one letter) see
Correspondence of Sir R.A. Fisher: Calendar of Correspondence with Allan Birnbaum
{{DEFAULTSORT:Birnbaum, Allan 1923 births 1976 deaths Writers from San Francisco UC Berkeley College of Letters and Science alumni American people of Russian-Jewish descent Academics of City, University of London Fellows of the American Statistical Association Scientists from the San Francisco Bay Area American science writers 20th-century American mathematicians 20th-century American non-fiction writers Courant Institute of Mathematical Sciences faculty 1976 suicides American mathematical statisticians Suicides in the United Kingdom