- Person
- Abraham Wald
- Lived
- 1902–1950
- Field
- Statistics
- From
- Hungarian-American
The story
Abraham Wald was born in 1902 in Kolozsvár, Hungary, now Cluj-Napoca in Romania, into a religious Jewish family; he was the grandson of Rabbi Moshe Shmuel Glasner. Unable as a Jew to obtain an academic post in 1930s Vienna, he left Austria after the Nazi annexation in 1938 and joined Columbia University in New York, where he stayed until his death.
During the Second World War Wald was a member of the Statistical Research Group at Columbia, a team of about 18 researchers, including Milton Friedman, Frederick Mosteller and Leonard Jimmie Savage, that applied statistics to military problems. One problem was the damage on aircraft returning from missions, with the goal of advising how to reduce bomber losses to enemy fire.
The difficulty was that the data came only from planes that had made it back. Aircraft shot down over enemy territory left no record of where they had been hit. Wald saw that this missing information was the heart of the problem. If returning planes rarely showed hits in a particular area, that did not mean the area was seldom hit; it was more likely that planes hit there did not return. He derived a way to estimate the damage distribution for all aircraft that flew, including those lost, from the damage on those that survived.
The group issued eight memoranda on analysing data from damaged combat aircraft. Wald's memorandum of 1943, A Method of Estimating Plane Vulnerability Based on Damage of Survivors, set out how to estimate the vulnerability of different parts of an aircraft, and he suggested that its conclusions could guide where to place protective armour. His work is considered seminal in operational research, then a young discipline.
Today Wald's bombers are the classic textbook example of survivorship bias: the error of drawing conclusions only from the cases that made it through a selection process. The same trap appears, for example, when financial studies leave out companies and funds that failed and so no longer exist, making the survivors look better than the whole group really performed. Wald also founded the field of sequential analysis and laid the foundations of statistical decision theory. He died with his wife in a plane crash in India in 1950, while on a lecture tour at the invitation of the Indian government.
Why it matters
Wald's analysis was aimed at protecting bomber crews, and it remains a basic lesson for anyone who draws conclusions from incomplete data.
About Abraham Wald
Refugee mathematician who founded sequential analysis and statistical decision theory, and whose wartime study of damaged bombers became the classic lesson in survivorship bias.
More about Abraham Wald
- Abraham Wald invented the test that can stop earlyDuring the Second World War, Abraham Wald created sequential analysis, a way to check evidence after each test and stop as soon as it is conclusive, often with far fewer observations.
- Abraham Wald gave early proofs that markets can balanceBarred from academic jobs in 1930s Vienna, Abraham Wald turned to economics and produced some of the first rigorous proofs that a competitive economic equilibrium can exist.
- Abraham Wald fled the Nazis and helped America win the warAbraham Wald escaped Austria in 1938; of nine relatives left behind, all but one were murdered at Auschwitz. In America he put his mathematics to work for the Allied war effort.
- Abraham Wald turned statistics into a science of decisionsIn a 1939 paper and his 1950 book Statistical Decision Functions, Abraham Wald recast statistics as the problem of making decisions under uncertainty when mistakes have costs.
- Statisticians use Abraham Wald's tools every dayThe Wald test, the Wald–Wolfowitz runs test, Wald's equation and the Wald distribution are among the everyday statistical tools that bear Abraham Wald's name.
Sources
- Abraham Wald Wikipedia
- Abraham Wald biography MacTutor History of Mathematics, University of St Andrews
- Survivorship bias Wikipedia
Another act of tikkun olam. This is part of tikkun olam, the Jewish idea of repairing the world, and every one of us can add to it.