Bernard Koopman

Bernard Osgood Koopman (1900 – August 18, 1981) was a French-born American mathematician, known for his work in ergodic theory, the foundations of probability, statistical theory and operations research.

After living in France and Italy, the Koopmans immigrated 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.

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.

Koopman's mother was a first cousin of William Fogg Osgood.

Publications

• "Hamiltonian Systems and Transformations in Hilbert Space" Proceedings of the National Academy of Sciences 17, 315–318, 1931.
• "On distributions admitting a sufficient statistic. Transactions of the American Mathematical Society, 39:399–409, 1936. This is the paper in which the Pitman–Koopman theorem, sometimes called the Pitman–Koopman–Darmois theorem, appeared.
• "The axioms and algebra of intuitive probability", Annals of Mathematics 41, 269–292, 1940.
• "The bases of probability", Bulletin of the American Mathematical Society, 46, 763–774, 1940.
• "Intuitive probabilities and sequences", Annals of Mathematics 42, 169–187, 1941.
• Search and Screening, first edition 1946.

Further reading

• Morse, Philip M. (1982), "In Memoriam: Bernard Osgood Koopman, 1900–1981", Operations Research 30 (3): viii+417–427, doi:10.1287/opre.30.3.417, JSTOR 170181 .

External links

• Worth reading: Search and Screening
• Bernard Koopman at the Mathematics Genealogy Project.