Abraham Wald | |
|---|---|
 A young Wald | |
| Born | (1902-10-31)October 31, 1902 |
| Died | December 13, 1950(1950-12-13) (aged 48) |
| Alma mater | King Ferdinand I University University of Vienna |
| 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 |
| Scientific career | |
| Fields | Mathematics Statistics Economics |
| Institutions | Columbia University Cowles Commission for Research in Economics |
| Doctoral advisor | Karl Menger |
| Doctoral students | Herman Chernoff Meyer Abraham Girshick Milton Sobel Charles Stein |
Abraham Wald (/wɔːld/;German:[valt];Hungarian:Wald Ábrahám,Yiddish:אברהם וואַלד;(1902-10-31)31 October 1902 –(1950-12-13)13 December 1950) was a Hungarian and American mathematician and statistician who contributed todecision theory,[1]geometry andeconometrics, and founded the field ofsequential analysis.[2] One of his well-known statistical works was written duringWorld War II on how to minimize the damage to bomber aircraft and took into account thesurvivorship bias in his calculations.[3] He spent his research career atColumbia University. He was the grandson of RabbiMoshe Shmuel Glasner.
Wald was born on 31 October 1902 inKolozsvár,Transylvania, in theKingdom of Hungary. A religiousJew, he did not attend school on Saturdays, as was then required by the Hungarian school system, and so he washomeschooled by his parents until college.[2] His parents were quite knowledgeable and competent as teachers.[4]
In 1928, he graduated in mathematics from theKing Ferdinand I University.[5] In 1927, he had enteredgraduate school at theUniversity of Vienna, from which he graduated in 1931 with a Ph.D. in mathematics. His advisor there wasKarl 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. WhenNazi Germanyannexed Austria in 1938, the discrimination against Jews intensified. In particular, Wald and his family were persecuted as Jews. Wald emigrated to theUnited States at the invitation of theCowles Commission for Research in Economics, to work on econometrics research.[2] By September 1938 Wald was a Fellow of the Carnegie Corporation at Columbia University learning about modern English language statistics fromHarold Hotelling. He was appointed to the Columbia Faculty in 1941 and remained there until his death.
DuringWorld War II, Wald was a member of theStatistical Research Group (SRG) atColumbia University, where he applied his statistical skills to various wartime problems.[6] There was a difficulty: the work was secret and Wald was officially an enemy alien and, as such, barred from access to restricted matter. Hotelling recounts, “This impasse led to a facetious suggestion that each page he wrote should immediately be snatched away and never shown to him again, but was resolved when a federal court granted him a hearing long before his turn on the docket and promptly naturalized him.”[7]
The problems that the SRG worked on included methods of sequential analysis and sampling inspection.[6] Another was to examine the distribution ofdamage 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.[3][8] His work is considered seminal in the discipline ofoperational research, which was then fledgling.
Wald and his wife died in 1950 when theAir India plane (VT-CFK, a DC-3 aircraft[9]) in which they were travelling crashed near theRangaswamy Pillar in the northern part of theNilgiri Mountains, in southernIndia, on an extensive lecture tour at the invitation of the Indian government.[2] He had visited theIndian 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.[10]
After his death, Wald was criticized by SirRonald A. FisherFRS. 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 andFrank Yates.[11] Wald's work was defended byJerzy Neyman the next year. Neyman explained Wald's work, particularly with respect to the design of experiments.[12]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."[13]
He is the father of the noted American physicistRobert Wald.
For a complete list, see"The Publications of Abraham Wald",Annals of Mathematical Statistics,23 (1):29–33, 1952,doi:10.1214/aoms/1177729483
