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Abraham Wald (; hu, Wald Ábrahám, yi, אברהם וואַלד;  – ) was a
Jewish Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...
Hungarian
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...
who contributed to
decision theory Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical ...
,
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, and
econometrics Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8 ...
and founded the field of statistical
sequential analysis In statistics, sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data are evaluated as they are collected, and further sampling is stopped in accordance with a pre- ...
. One of his well-known statistical works was written 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 ...
on how to minimize the damage to bomber aircraft and took into account the survivorship bias in his calculations. He spent his research career at
Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...
.


Life and career

Wald was born on 31 October 1902 in
Kolozsvár ; hu, kincses város) , official_name=Cluj-Napoca , native_name= , image_skyline= , subdivision_type1 = County , subdivision_name1 = Cluj County , subdivision_type2 = Status , subdivision_name2 = County seat , settlement_type = City , l ...
,
Transylvania Transylvania ( ro, Ardeal or ; hu, Erdély; german: Siebenbürgen) is a historical and cultural region in Central Europe, encompassing central Romania. To the east and south its natural border is the Carpathian Mountains, and to the west the Ap ...
, in the
Kingdom of Hungary The Kingdom of Hungary was a monarchy in Central Europe that existed for nearly a millennium, from the Middle Ages into the 20th century. The Principality of Hungary emerged as a Christian kingdom upon the coronation of the first king Stephen ...
. A religious
Jew Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""Th ...
, he did not attend school on Saturdays, as was then required by the Hungarian school system, and so he was thus
homeschooled Homeschooling or home schooling, also known as home education or elective home education (EHE), is the education of school-aged children at home or a variety of places other than a school. Usually conducted by a parent, tutor, or an onlin ...
by his parents until college. His parents were quite knowledgeable and competent as teachers. In 1928, he graduated in mathematics from the King Ferdinand I University. In 1927, he entered graduate school at the
University of Vienna The University of Vienna (german: Universität Wien) is a public research university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world. With its long and rich histor ...
, from which he graduated in 1931 with a Ph.D. in mathematics. His advisor there was
Karl Menger Karl Menger (January 13, 1902 – October 5, 1985) was an Austrian-American mathematician, the son of the economist Carl Menger. In mathematics, Menger studied the theory of algebras and the dimension theory of low- regularity ("rough") curves ...
. Despite Wald's brilliance, he could not obtain a university position because of Austrian discrimination against Jews. However,
Oskar Morgenstern Oskar Morgenstern (January 24, 1902 – July 26, 1977) was an Austrian-American economist. In collaboration with mathematician John von Neumann, he founded the mathematical field of game theory as applied to the social sciences and strategic decis ...
created a position for Wald in economics. When
Nazi Germany Nazi Germany (lit. "National Socialist State"), ' (lit. "Nazi State") for short; also ' (lit. "National Socialist Germany") (officially known as the German Reich from 1933 until 1943, and the Greater German Reich from 1943 to 1945) was ...
annexed Austria in 1938, the discrimination against Jews intensified. In particular, Wald and his family were persecuted as Jews. Wald immigrated to the
United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...
at the invitation of the
Cowles Commission for Research in Economics The Cowles Foundation for Research in Economics is an economic research institute at Yale University. It was created as the Cowles Commission for Research in Economics at Colorado Springs in 1932 by businessman and economist Alfred Cowles. In 193 ...
, to work on econometrics research. 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 ...
, Wald was a member of the Statistical Research Group (SRG) at
Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...
, where he applied his statistical skills to various wartime problems. They included methods of sequential analysis and sampling inspection. One of the problems that the SRG worked on was to examine the distribution of damage to aircraft returning after flying missions to provide advice on how to minimize bomber losses to enemy fire. Wald derived a useful means of estimating the damage distribution for all aircraft that flew from the data on the damage distribution of all aircraft that returned. His work is considered seminal in the discipline of
operational 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 ...
, which was then fledgling. Wald and his wife died in 1950 when the Air India plane (VT-CFK, a DC-3 aircraft) in which they were travelling crashed near the Rangaswamy Pillar in northern part of the
Nilgiri Mountains The Nilgiri Mountains form part of the Western Ghats in northwestern Tamil Nadu, Southern Karnataka, and eastern Kerala in India. They are located at the trijunction of three states and connect the Western Ghats with the Eastern Ghats. At le ...
, in southern
India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...
, on an extensive lecture tour at the invitation of the Indian government. He had visited the
Indian Statistical Institute Indian Statistical Institute (ISI) is a higher education and research institute which is recognized as an Institute of National Importance by the 1959 act of the Indian parliament. It grew out of the Statistical Laboratory set up by Prasanta ...
at Calcutta and was to attend the Indian Science Congress at Bangalore in January. Their two children were back at home in the United States. After his death, Wald was criticized by Sir Ronald A. Fisher FRS. Fisher attacked Wald for being a mathematician without scientific experience who had written an incompetent book on statistics. Fisher particularly criticized Wald's work on the design of experiments and alleged ignorance of the basic ideas of the subject, as set out by Fisher and Frank Yates. (criticism of statistical theories of
Jerzy Neyman Jerzy Neyman (April 16, 1894 – August 5, 1981; born Jerzy Spława-Neyman; ) was a Polish mathematician and statistician who spent the first part of his professional career at various institutions in Warsaw, Poland and then at University College ...
and Abraham Wald)
Wald's work was defended by
Jerzy Neyman Jerzy Neyman (April 16, 1894 – August 5, 1981; born Jerzy Spława-Neyman; ) was a Polish mathematician and statistician who spent the first part of his professional career at various institutions in Warsaw, Poland and then at University College ...
the next year. Neyman explained Wald's work, particularly with respect to the design of experiments. (reply to Fisher 1955)
Lucien Le Cam Lucien Marie Le Cam (November 18, 1924 – April 25, 2000) was a mathematician and statistician. Biography Le Cam was born November 18, 1924 in Croze, France. His parents were farmers, and unable to afford higher education for him; his father die ...
credits him in his own book, ''Asymptotic Methods in Statistical Decision Theory'': "The ideas and techniques used reflect first and foremost the influence of Abraham Wald's writings." He was the father of the noted American physicist
Robert Wald The name Robert is an ancient Germanic given name, from Proto-Germanic "fame" and "bright" (''Hrōþiberhtaz''). Compare Old Dutch ''Robrecht'' and Old High German ''Hrodebert'' (a compound of '' Hruod'' ( non, Hróðr) "fame, glory, honou ...
.


Notable publications

For a complete list, see * * * * * *


References


Further reading

* *


External links

* {{DEFAULTSORT:Wald, Abraham 1902 births 1950 deaths Scientists from Cluj-Napoca Austro-Hungarian Jews Jewish emigrants from Austria to the United States after the Anschluss Presidents of the Institute of Mathematical Statistics Fellows of the American Statistical Association American statisticians Hungarian statisticians Econometricians 20th-century American mathematicians Columbia University faculty Jewish American scientists Victims of aviation accidents or incidents in India 20th-century Hungarian mathematicians Babeș-Bolyai University alumni University of Vienna alumni Mathematical economists Hungarian operations researchers Functional analysts American operations researchers 20th-century Hungarian economists Fellows of the Econometric Society Mathematical statisticians