Abraham Wald Explained

Abraham Wald
Birth Date:31 October 1902
Birth Place:Kolozsvár, Kingdom of Hungary, Austria-Hungary
Death Place:Nilgiri Mountains, India
Field:Mathematics
Statistics
Economics
Work Institutions:Columbia University
Cowles Commission for Research in Economics
Alma Mater:King Ferdinand I University
University of Vienna
Doctoral Advisor:Karl Menger
Doctoral Students:Herman Chernoff
Meyer Abraham Girshick
Milton Sobel
Charles Stein
Known For:Wald's equation
Wald test
Wald distribution
Wald–Wolfowitz runs test
Wald's martingale
Wald's maximin model
Mann–Wald theorem
Decision theory
Sequential analysis
Sequential probability ratio test
Children:Robert Wald

Abraham Wald (; Hungarian: Wald Ábrahám, Yiddish: אברהם וואַלד; 31 October 1902 –) was a Jewish Hungarian mathematician who contributed to decision theory[1], geometry and econometrics, and founded the field of sequential analysis.[2] One of his well-known statistical works was written during World War II on how to minimize the damage to bomber aircraft and took into account the survivorship bias in his calculations.[3] He spent his research career at Columbia University. He was the grandson of Rabbi Moshe Shmuel Glasner.

Life and career

Wald was born on 31 October 1902 in Kolozsvár, Transylvania, in the Kingdom of Hungary. A religious Jew, he did not attend school on Saturdays, as was then required by the Hungarian school system, and so he was homeschooled by his parents until college.[2] His parents were quite knowledgeable and competent as teachers.

In 1928, he graduated in mathematics from the King Ferdinand I University.[4] In 1927, he had entered graduate school at the University of Vienna, from which he graduated in 1931 with a Ph.D. in mathematics. His advisor there was Karl Menger[2] [1] .

Despite Wald's brilliance, he could not obtain a university position because of Austrian discrimination against Jews. However, Oskar Morgenstern created a position for Wald in economics. When Nazi Germany 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 at the invitation of the Cowles Commission for Research in Economics, to work on econometrics research.[2]

During World War II, Wald was a member of the Statistical Research Group (SRG) at Columbia University, where he applied his statistical skills to various wartime problems.[5] 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.[6] His work is considered seminal in the discipline of operational research, which was then fledgling.

Wald and his wife died in 1950 when the Air India plane (VT-CFK, a DC-3 aircraft[7]) in which they were travelling crashed near the Rangaswamy Pillar in the northern part of the Nilgiri Mountains, in southern India, on an extensive lecture tour at the invitation of the Indian government.[2] He had visited the Indian Statistical Institute 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.[8]

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.[9] Wald's work was defended by Jerzy Neyman the next year. Neyman explained Wald's work, particularly with respect to the design of experiments.[10] Lucien Le Cam 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."[11]

He was the father of the noted American physicist Robert Wald.

Notable publications

For a complete list, see

Further reading

Notes and References

  1. Duppe, Till . Till Duppe . Weintraub, E. Roy . E. Roy Weintraub . History of Political Economy . 48 . 191 . 635--655 . 2015 . Losing Equilibrium: On the Existence of Abraham Wald's Fixed-Point Proof of 1935 . Econometrica, Vol. 19, No. 4 . 10.1215/00182702-3687283. 10419/149731 . free .
  2. 10.2307/1907462 . Morgenstern, Oskar . Oskar Morgenstern . Econometrica . 19 . 4 . 361–367 . 1951 . Abraham Wald, 1902–1950 . Econometrica, Vol. 19, No. 4 . 1907462.
  3. Mangel . Marc . Samaniego . Francisco J. . Abraham Wald's Work on Aircraft Survivability . Journal of the American Statistical Association . June 1984 . 79 . 386 . 259–267 . 10.1080/01621459.1984.10478038 . . 2288257.
  4. Anuarul Universității Regele Ferdinand I pe anul școlar 1927/28. p. 187. Online access, University Library in Cluj, Romania.
  5. 10.1080/01621459.1980.10477469 . 75 . 370 . The Statistical Research Group, 1942–1945 . Journal of the American Statistical Association . 320–330. 1980 . Wallis . W. Allen . 2287451.
  6. Wald . Abraham . A Reprint of 'A Method of Estimating Plane Vulnerability Based on Damage of Survivors' . ADA091073 . . . 1980 . 1943 . https://web.archive.org/web/20210512125414/https://apps.dtic.mil/sti/pdfs/ADA091073.pdf. live. May 12, 2021.
  7. Web site: Aircraft accident Douglas C-47B-5-DK (DC-3) VT-CFK Kotagiri . . . 26 September 2021.
  8. News: Prof. Wald Reported Among Victims of India Plane Crash. 15 December 1950. Columbia Daily Spectator. 2018-02-08. 52. XCV. 1.
  9. Statistical methods and scientific induction. Ronald A. Fisher . Ronald . Fisher. Journal of the Royal Statistical Society, Series B. 17. 1955. 69–78. 2983785. 1. 10.1111/j.2517-6161.1955.tb00180.x . (criticism of statistical theories of Jerzy Neyman and Abraham Wald)
  10. Note on an Article by Sir Ronald Fisher. Jerzy Neyman . Jerzy . Neyman. Journal of the Royal Statistical Society, Series B. 18. 1956. 288–294. 2983716. 2. 10.1111/j.2517-6161.1956.tb00236.x . (reply to Fisher 1955)
  11. Book: Le Cam , Lucien . Asymptotic Methods in Statistical Decision Theory. Lucien Le Cam . 1986. xiii.