Bernard Koopman
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Bernard Osgood Koopman (January 19, 1900 – August 18, 1981) was a French-born American mathematician, known for his work in
ergodic theory Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expres ...
, the foundations of probability,
statistical theory The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistica ...
and
operations research Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve deci ...
.


Education and work

After living in France and Italy, Koopman emigrated to the United States in 1915. Koopman was a student of
George David Birkhoff George David Birkhoff (March 21, 1884 – November 12, 1944) was an American mathematician best known for what is now called the ergodic theorem. Birkhoff was one of the most important leaders in American mathematics in his generation, and durin ...
and his initial work concentrated on
dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space. Examples include the mathematical models that describe the swinging of a ...
s and
mathematical physics Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...
. In 1931/1932, Koopman and
John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...
proposed a Hilbert space formulation of classical mechanics, known as the
Koopman–von Neumann classical mechanics The Koopman–von Neumann mechanics is a description of classical mechanics in terms of Hilbert space, introduced by Bernard Koopman and John von Neumann in 1931 and 1932, respectively. As Koopman and von Neumann demonstrated, a Hilbert space of c ...
. During
World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
, he joined the Anti-Submarine Warfare Operations Research Group (ASWORG, later ORG) in
Washington, D.C. ) , image_skyline = , image_caption = Clockwise from top left: the Washington Monument and Lincoln Memorial on the National Mall, United States Capitol, Logan Circle, Jefferson Memorial, White House, Adams Morgan, ...
, directed by
Philip M. Morse Philip McCord Morse (August 6, 19035 September 1985), was an American physicist, administrator and pioneer of operations research (OR) in World War II. He is considered to be the father of operations research in the U.S. Biography Morse graduat ...
, to work for the U.S. Navy.
Philip M. Morse Philip McCord Morse (August 6, 19035 September 1985), was an American physicist, administrator and pioneer of operations research (OR) in World War II. He is considered to be the father of operations research in the U.S. Biography Morse graduat ...
: ''In memoriam: Bernard Osgood Koopman, 1900–1981'', Operations Research, Vol. 30, No. 3 (May - Jun., 1982), pp. viii+417-427. Published by:
Institute for Operations Research and the Management Sciences The Institute for Operations Research and the Management Sciences (INFORMS) is an international society for practitioners in the fields of operations research (O.R.), management science, and analytics. It was established in 1995 with the merger of ...
(INFORMS),
jstor 170181
The work of Koopman and his colleagues at ASWORG concerned the development of techniques for the
US Navy The United States Navy (USN) is the maritime service branch of the United States Armed Forces and one of the eight uniformed services of the United States. It is the largest and most powerful navy in the world, with the estimated tonnage of ...
to hunt
U-boat U-boats were naval submarines operated by Germany, particularly in the First and Second World Wars. Although at times they were efficient fleet weapons against enemy naval warships, they were most effectively used in an economic warfare role ...
s. The theoretical work laid the foundations for
search theory In microeconomics, search theory studies buyers or sellers who cannot instantly find a trading partner, and must therefore search for a partner prior to transacting. Search theory clarifies how buyers and sellers choose when to acknowledge a coo ...
which subsequently became a field of its own within
operations research Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve deci ...
. 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 The Institute for Operations Research and the Management Sciences (INFORMS) is an international society for practitioners in the fields of operations research (O.R.), management science, and analytics. It was established in 1995 with the merger o ...
. He wrote down the results in detailed form in the book ''Search and Screening'' which was declassified in 1958.Laura H. Nunn
An introduction to the literature on search theory
, Professional Paper 305, June 1981, Center for Naval Analyses (CNA) Corporation (accessed 31.01.2012)
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 In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate ...
states that the only families of probability distributions that admit a
sufficient statistic In statistics, a statistic is ''sufficient'' with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample provides any additional information as to the value of the pa ...
whose dimension remains bounded as the sample size increases are
exponential families In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate ...
.


Family

Koopman had two daughters from his first wife Mary Louise Harvey who died in 1946. In 1948 he married Jane Bridgman, daughter of his Harvard professor of thermodynamics,
Percy Williams Bridgman Percy Williams Bridgman (April 21, 1882 – August 20, 1961) was an American physicist who received the 1946 Nobel Prize in Physics for his work on the physics of high pressures. He also wrote extensively on the scientific method and on other as ...
, and they had three more daughters. Koopman's mother, née Louise Osgood, was a first cousin of
William Fogg Osgood William Fogg Osgood (March 10, 1864, Boston – July 22, 1943, Belmont, Massachusetts) was an American mathematician. Education and career In 1886, he graduated from Harvard, where, after studying at the universities of Göttingen (1887–188 ...
, and his father, Augustus Koopman (1869-1914), was a well known painter.


Publications

* * This is the paper in which the
Pitman–Koopman theorem In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculat ...
, sometimes called the
Pitman–Koopman–Darmois theorem In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate ...
, appeared. * "The axioms and algebra of intuitive probability", ''
Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the ...
'' 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 (classified ''Confidential'', declassified in 1958).


References


Further reading

*


External links


Worth reading: Search and Screening

Biography of Bernard Koopman
from the Institute for Operations Research and the Management Sciences {{DEFAULTSORT:Koopman, Bernard O. 1900 births 1981 deaths 20th-century American mathematicians American operations researchers American statisticians Harvard University alumni Columbia University faculty French emigrants to the United States United States Navy personnel of World War II United States Navy civilians