After living in France and Italy, Koopman emigrated to the United States in 1915. Koopman was a student of
George David Birkhoff and his initial work concentrated on
dynamical systems and
mathematical physics. In 1931/1932, Koopman and
John von Neumann proposed a Hilbert space formulation of classical mechanics, known as the
Koopman–von Neumann classical mechanics. During
World War II, he joined the Anti-Submarine Warfare Operations Research Group (ASWORG, later ORG) in
Washington, D.C., directed by
Philip M. Morse, to work for the U.S. Navy. The work of Koopman and his colleagues at ASWORG concerned the development of techniques for the
US Navy to hunt
U-boats. The theoretical work laid the foundations for
search theory which subsequently became a field of its own within
operations research. Their results remained classified
Confidential for many years after the war; after 1955 Koopman set out to publish three articles on easily declassifiable portions of the work in the Journal of the
Operations Research Society of America. He wrote down the results in detailed form in the book
Search and Screening which was declassified in 1958. A large part of his work is a systematization of the work performed by his group at ASWORG; the portions on optimum allocation of search effort and on probabilistic aspects of search theory were developed by Koopman himself. The
Pitman–Koopman–Darmois theorem states that the only families of probability distributions that admit a
sufficient statistic whose dimension remains bounded as the sample size increases are
exponential families. ==Family==