Abraham Wald

From Wikipedia, the free encyclopedia
Abraham Wald
A young Wald
Born(1902-10-31)October 31, 1902
DiedDecember 13, 1950(1950-12-13) (aged 48)
Alma materKing Ferdinand I University
University of Vienna
Known forWald'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
ChildrenRobert Wald
Scientific career
InstitutionsColumbia University
Cowles Commission for Research in Economics
Doctoral advisorKarl Menger
Doctoral studentsHerman Chernoff
Milton Sobel
Charles Stein

Abraham Wald (/wɔːld/; Hungarian: Wald Ábrahám, Yiddish: אברהם וואַלד; (1902-10-31)31 October 1902 – (1950-12-13)13 December 1950) was a Jewish Hungarian mathematician who contributed to decision theory, geometry and econometrics, and founded the field of sequential analysis.[1] 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.[2] He spent his research career at Columbia University. He was the grandson of Rabbi Moshe Shmuel Glasner.

Life and career[edit]

Photograph of Abraham Wald from the Oberwolfach Research Institute for Mathematics

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.[1] His parents were quite knowledgeable and competent as teachers.[3]

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.[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.[1]

The damaged portions of returning planes show locations where they can sustain damage and still return home; those hit in other places presumedly do not survive. (Image shows hypothetical data.)

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.[5] 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.[2][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.[1] 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[edit]

For a complete list, see "The Publications of Abraham Wald", Annals of Mathematical Statistics, 23 (1): 29–33, 1952, doi:10.1214/aoms/1177729483


  1. ^ a b c d e Morgenstern, Oskar (1951). "Abraham Wald, 1902–1950". Econometrica. Econometrica, Vol. 19, No. 4. 19 (4): 361–367. doi:10.2307/1907462. JSTOR 1907462.
  2. ^ a b Mangel, Marc; Samaniego, Francisco J. (June 1984). "Abraham Wald's Work on Aircraft Survivability" (PDF). Journal of the American Statistical Association. American Statistical Association. 79 (386): 259–267. doi:10.1080/01621459.1984.10478038. JSTOR 2288257.
  3. ^ O'Connor, John J.; Robertson, Edmund F., "Abraham Wald", MacTutor History of Mathematics Archive, University of St Andrews
  4. ^ Anuarul Universității Regele Ferdinand I pe anul școlar 1927/28. p. 187. Online access, University Library in Cluj, Romania.
  5. ^ a b Wallis, W. Allen (1980). "The Statistical Research Group, 1942–1945". Journal of the American Statistical Association. 75 (370): 320–330. doi:10.1080/01621459.1980.10477469. JSTOR 2287451.
  6. ^ Abraham, Wald (1980) [1943]. A Reprint of 'A Method of Estimating Plane Vulnerability Based on Damage of Survivors' (PDF) (Technical report). Center for Naval Analyses; Statistical Research Group, National Defense Research Committee. ADA091073. Archived (PDF) from the original on May 12, 2021 – via Defense Technical Information Center.
  7. ^ "Aircraft accident Douglas C-47B-5-DK (DC-3) VT-CFK Kotagiri". Aviation Safety Network. Flight Safety Foundation. 26 September 2021.
  8. ^ "Prof. Wald Reported Among Victims of India Plane Crash". Columbia Daily Spectator. Vol. XCV, no. 52. 15 December 1950. p. 1. Retrieved 2018-02-08.
  9. ^ Fisher, Ronald (1955). "Statistical methods and scientific induction". Journal of the Royal Statistical Society, Series B. 17 (1): 69–78. JSTOR 2983785. (criticism of statistical theories of Jerzy Neyman and Abraham Wald)
  10. ^ Neyman, Jerzy (1956). "Note on an Article by Sir Ronald Fisher". Journal of the Royal Statistical Society, Series B. 18 (2): 288–294. JSTOR 2983716. (reply to Fisher 1955)
  11. ^ Le Cam, Lucien (1986). Asymptotic Methods in Statistical Decision Theory. pp. xiii.
  12. ^ Robbins, Herbert (1951), "Review: A. Wald, Statistical decision functions", Bull. Amer. Math. Soc., 57 (5): 383–384, doi:10.1090/S0002-9904-1951-09520-8

Further reading[edit]

External links[edit]