Birnbaum was born in
San Francisco. His parents were Russian-born Orthodox Jews. He studied mathematics at the
University of California, Berkeley, 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 "Fundamentals of statistical inference" (with
Adrian Smith). 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 theorem which argued 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 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 ==