Statisticians use Abraham Wald's tools every day

Person: Abraham Wald
Lived: 1902–1950
Field: Statistics
From: Hungarian-American

The story

Few mathematicians have their names attached to as many working tools as Abraham Wald. Born in 1902 in Kolozsvár, now Cluj-Napoca in Romania, and trained as a geometer in Vienna, he arrived at Columbia University in 1938 as a refugee and died in a plane crash in India in 1950. In barely twelve years in America he contributed ideas that statisticians still use constantly.

The Wald test is one of the three classical ways of testing a statistical hypothesis, alongside the likelihood-ratio test and the Lagrange multiplier test. It measures how far an estimated value lies from the value a hypothesis predicts, weighted by the precision of the estimate, and it is widely used, for example in regression analysis, to judge whether an estimated effect is real. Its practical advantage is that only the unrestricted model needs to be estimated.

The Wald–Wolfowitz runs test, named for Wald and his longtime collaborator Jacob Wolfowitz, checks whether a two-valued sequence of data, such as pluses and minuses, is random by counting its runs of repeated values. Wald's equation, also called Wald's identity, is a basic result in probability theory: it gives the expected total of a random number of random quantities, a tool used throughout probability and statistics. The inverse Gaussian distribution, also known as the Wald distribution, is a standard probability distribution, used for example in psychology to model response times. Wald's maximin model, which ranks decisions by their worst-case outcomes, is a reference point in robust decision-making. His 1940 paper on fitting a straight line when both variables are measured with error addressed a practical problem faced in every experimental science.

Wald also helped make Columbia a centre of mathematical statistics. His lectures were famous for their clarity, and his students' notes circulated to universities across the United States. Among his doctoral students were Charles Stein, who earned his PhD at Columbia in 1947 and became known for Stein's paradox, and Herman Chernoff, who completed his PhD at Brown University under Wald's supervision in 1948. A student remembered him as a quiet and gentle man, deeply immersed in his work. His son Robert Wald became a noted American physicist.

Why it matters

Wald's methods are built into the software and textbooks used by scientists, doctors and economists worldwide.

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.

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Abraham Wald

1902–1950 · Statistics

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