Abraham Wald Concepts

AIQ: How People and Machines Are Smarter Together

by Nick Polson and James Scott · 14 May 2018 · 301pp · 85,126 words

massive data sets in which you are the conditioning event. In this chapter, you’ll learn a bit of the magic behind how this works. Abraham Wald, World War II Hero The core idea behind personalization is a lot older than Netflix, older even than television itself. In fact, if you want

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. 2. Their fighter escorts: the Spitfires and P-51 Mustangs sent along to defend the bombers from the Luftwaffe. 3. A Hungarian-American statistician named Abraham Wald. Abraham Wald never shot down a Messerschmitt or even saw the inside of a combat aircraft. Nonetheless, he made an outsized contribution to the Allied war effort

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, Hulu, Spotify, Instagram, Amazon, YouTube, and just about every tech company that’s ever made you an automatic suggestion worth following. Wald’s Early Years Abraham Wald was born in 1902 to a large Orthodox Jewish family in Kolozsvár, Hungary, which became part of Romania and changed its name to Cluj after

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life. Yet he would remain so stricken by grief over the fate of his family that he never again played the violin. Wald in America Abraham Wald would, however, do more than his fair share to make sure that Hitler faced the music. The 35-year-old Wald arrived in America in

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: Albert Einstein, John von Neumann, Edward Teller, Stanislaw Ulam, and hundreds of other brilliant refugees who gave American science a decisive boost during the war. Abraham Wald, too, was eager to answer the call. He was soon given the chance, when his colleague W. Allen Wallis invited him to join Columbia’s

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American Association for the Advancement of Science. Milton Friedman and George Stigler received the Nobel Prize in Economics. And on this team of all-stars, Abraham Wald was like LeBron James: the man who did everything. Only the hardest problems ever found their way to his desk, for even his fellow geniuses

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still used today. But our story here, about the exponential growth of Netflix-style personalization, relates to a different and almost universally misunderstood contribution of Abraham Wald’s: his method for devising personalized survivability recommendations for aircraft. Every day, the Allied air forces sent massive squadrons of airplanes to attack Nazi targets

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notable exception of an obscure, highly technical paper published in the Journal of the American Statistical Association in 1984—gets it wrong.6 Try Googling “Abraham Wald” and “World War II” yourself and see what you find: one blog post after another about how a mathematical crusader named Wald prevented those navy

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bullet holes were on the fuselage. The navy guys reached the obvious conclusion: put more armor on the fuselage. Nonetheless, they gave their data to Abraham Wald, just to double-check. Wald’s little gray cells went to work. And then a thunderbolt. “Wait!” Wald exclaims. “That’s wrong. We don’t

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basis in fact. Worse still, this embellished version, in which the moral of the story is about survivorship bias, misses the truly important thing about Abraham Wald’s contribution to the Allied war effort. Survivorship bias in the data was obviously the problem, and everybody knew it. Otherwise there would have been

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didn’t know how to do this. They were really smart, but it is no insult to say that they weren’t as smart as Abraham Wald. Wald’s real contribution was far subtler and more interesting than delivering some survivorship-bias boom-shakalaka to a cartoonish dolt of a navy commander

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Stratofortress, the longest-serving aircraft in U.S. military history. Missing Data: What You Don’t Know Can Fool You As you can now appreciate, Abraham Wald’s problem of improving aircraft survivability was a whole lot like Netflix’s problem of making personalized film suggestions. But there’s a catch, and

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personalize film recommendations for each viewer. But much of the data is missing: most subscribers haven’t watched most films.” The catch is that both Abraham Wald and Netflix needed to estimate a conditional probability, but both faced the problem of missing data. And sometimes what’s missing can be very informative

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the quotidian truth was revealed: ARMADILLO CARPET CARE Sometimes the missing part of the data changes the entire story. It was just the same with Abraham Wald’s data on aircraft survivability. Although his raw figures are lost to history, we can use his published navy report to hypothesize what he might

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(10-year winning streak | good stock picker) with P(good stock picker | 10-year winning streak). But remember our key lesson from the story of Abraham Wald: conditional probabilities aren’t symmetric like that. So is the fund manager lucky or good? Let’s run through the Bayesian calculation under two different

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, 1944, 1947, 1950), and Army Air Forces, Statistical Digest (World War II), available at https://archive.org/details/ArmyAirForcesStatisticalDigestWorldWarII. 4. Material on the life of Abraham Wald was drawn from the following sources: W. Allen Wallis, “The Statistical Research Group, 1942–1945,” Journal of the American Statistical Association 75, no. 370 (June

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1980): 320–30; Marc Mangel and Francisco J. Samaniego, “Abraham Wald’s Work on Aircraft Survivability,” Journal of the American Statistical Association 79, no. 386 (June 1984): 259–67, and see also “Comment” by James O

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. Berger (267–69) and “Rejoinder” by the authors (270–71); J. Wolfowitz, “Abraham Wald, 1902–1950,” Annals of Mathematical Statistics 23, no. 1 (1952): 1–13; Oskar Morgenstern, “Abraham Wald, 1902–1950,” Econometrica 19, no. 4 (Oct. 1951): 361–67; Karl Menger, “The Formative Years of

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Abraham Wald and His Work in Geometry,” Annals of Mathematical Statistics 23, no. 1 (1952): 14–20; L. Weiss, “Wald, Abraham,” in Leading

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in Statistical Sciences: From the Seventeenth Century to the Present, ed. Norman L. Johnson and Samuel Kotz (New York: John Wiley & Sons, 1997), 164–67; “Abraham Wald,” MacTutor History of Mathematics, http://www-history.mcs.st-andrews.ac.uk/Biographies/Wald.html. 5. W. Allen Wallis, “The Statistical Research Group, 1942–1945

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these terms. We have also left out a lot of technical detail. We encourage the interested reader to consult Marc Mangel and Francisco J. Samaniego, “Abraham Wald’s Work on Aircraft Survivability,” Journal of the American Statistical Association 79, no. 386 (June 1984): 259–67; see also “Comment” by James O. Berger

Black Box Thinking: Why Most People Never Learn From Their Mistakes--But Some Do

by Matthew Syed · 3 Nov 2015 · 410pp · 114,005 words

.” It involved the losses of bomber aircraft during World War II and was conducted by one of the most brilliant mathematicians of the twentieth century: Abraham Wald. His analysis was not just a pivotal moment in a major conflict, but also an important example within the context of this book. Learning from

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to learn from failure, you have to take into account not merely the data you can see, but also the data you can’t. III Abraham Wald was born in Hungary in 1902 to a Jewish baker. He was educated at home by his older brother, Martin, who was a qualified engineer

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armor and vehicle shielding and has led to major improvements in battlefield helmets, protective clothing, and medical equipment31 (just as the “black box” analysis by Abraham Wald improved the armoring of bombers during World War II). Before 2001, however, military personnel were rarely autopsied, meaning that the lessons were not surfaced—leaving

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understand why accidents happen has evolved over the last century and a half, in many remarkable and fascinating ways. 9. Oskar Morgenstern, Abraham Wald obituary, Econometrica, October 1951. 10. H. Freeman, “Abraham Wald,” in D. L. Sills (ed.), International Encyclopedia of Social Sciences, 16 (1968), 435–38. 11. Karl Menger, “The Formative Years of

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Abraham Wald and His Work in Geometry,” in Annals of Mathematical Statistics 23, no. 1 (1952): 14–20. 12. http://youarenotsosmart.com/tag/abraham-wald/. 13. Ibid. 14. Ibid. 15. https://hbr.org/2011/04/strategies-for-learning-from-failure

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. 16. http://cna.org/sites/default/files/research/0204320000.pdf. 17. Oskar Morgenstern, Abraham Wald obituary. CHAPTER 3: THE PARADOX OF SUCCESS 1. Information on United 1549 from investigation report (http://www.ntsb.gov/investigations/AccidentReports/Reports/AAR1003.pdf), two

Journey to the Edge of Reason: The Life of Kurt Gödel

by Stephen Budiansky · 10 May 2021 · 406pp · 108,266 words

members of the group, particularly with Georg Nöbeling, sometimes with Franz Alt and Olga Taussky, when she was in Vienna, and later on frequently with Abraham Wald and foreign visitors. He was a spirited participant in discussions on a large variety of topics. Orally, as well as in writing, he always expressed

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few friends whom Gödel ever addressed in his letters using the informal pronoun Du.44 Gödel’s other deepening professional friendship that year was with Abraham Wald. The son of an Orthodox Jewish baker, he had been educated at home because his family refused to allow him to attend the local public

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by now desperately looking for a situation, anywhere but home. Within a year Franz Alt would leave for the Econometrics Institute in New York City; Abraham Wald for the Cowles Commission for Research in Economics in Colorado Springs, Colorado; Friedrich Waismann for Cambridge University; Oskar Morgenstern for Princeton University. Karl Popper had

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was a terrible person, the doctors were impostors, evil spirits had removed from his desk a letter about his unfinished essay on Carnap, his friend Abraham Wald had actually not died in a plane crash nearly thirty years earlier but had survived and was secretly living in the Soviet Union. He had

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.Feferman and Feferman, Tarski, 5, 84–85, 144–45. 45.Karl Menger quoted in Sigmund, Exact Thinking, 230; Morgenstern, “Abraham Wald,” 361–62; OMD, 6 June 1936. 46.Menger, Reminiscences, 212–13; Morgenstern, “Abraham Wald,” 363. 47.Menger, Reminiscences, 214. 48.Menger, Reminiscences, 216. 49.Kreisel, “Kurt Gödel,” 154. 50.KG to Oswald Veblen

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Russell: The Spirit of Solitude, 1872–1921. New York: Free Press, 1996. —. Ludwig Wittgenstein: The Duty of Genius. 1990. New York: Penguin, 1991. Morgenstern, Oskar. “Abraham Wald, 1902–1950.” Econometrica 19, no. 4 (October 1951): 361–67. —. Diaries. Oskar Morgenstern Papers. Rare Book and Manuscript Library, Duke University, Durham, N.C. Digital

The Marginal Revolutionaries: How Austrian Economists Fought the War of Ideas

by Janek Wasserman · 23 Sep 2019 · 470pp · 130,269 words

for International Settlements. Spending more time with Karl Menger and his Mathematical Colloquium—where one could hear presentations not only from Menger but also from Abraham Wald, Kurt Gödel, Werner Heisenberg, Alfred Tarski, and Rudolf Carnap—Morgenstern took an interest in modern mathematics and its potential for improving economic theory. After Mises

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year later and in 1940 received a research fellowship at the Brookings Institution, with recommendations from Haberler and Morgenstern.9 The case of the mathematician Abraham Wald best reveals the extensiveness of the efforts of Austrian economists. Born in 1902 in Cluj in the Hungarian half of the Austro-Hungarian Empire (present

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the early 1930s. Morgenstern pivoted away from his earliest work on time and economic methodology under the influence of Karl Menger and through collaboration with Abraham Wald. He became convinced that advanced mathematics provided the way forward for economics. Upon arrival at Princeton, he struck up a fast friendship with the Hungarian

Work Rules!: Insights From Inside Google That Will Transform How You Live and Lead

by Laszlo Bock · 31 Mar 2015 · 387pp · 119,409 words

assumptions—guesses, really—about how things work in organizations. Most of these guesses are rooted in sample bias. A textbook illustration of sample bias is Abraham Wald’s work in World War II. Wald, a Hungarian mathematician, was a member of the Statistical Research Group (a group based at Columbia University that

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of St. Andrews). 99. Richard Norton Smith, “Ron Nessen,” Gerald R. Ford Oral History Project, http://geraldrfordfoundation.org/centennial/oralhistory/ron-nessen/. 100. “SciTech Tuesday: Abraham Wald, Seeing the Unseen,” post by Annie Tete, STEM Education Coordinator at the National World War II Museum, See & Hear (museum blog), November 13, 2012, http

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://www.nww2m.com/2012/11/scitech-tuesday-abraham-wald-seeing-the-unseen/. A reprint of Wald’s work can be found here: http://cna.org/sites/default/files/research/0204320000.pdf. 101. “Lawyercat” is

Theory of Games and Economic Behavior: 60th Anniversary Commemorative Edition (Princeton Classic Editions)

by John von Neumann and Oskar Morgenstern · 19 Mar 2007

included von Neumann and Morgenstern, visitors to the institute such as Irving Kaplansky, Ky Fan, and David Bourgin, as well as outside visitors such as Abraham Wald, the Columbia statistician who had made significant connections between game theory and statistical inference. (Wald had done the review of the TGEB for Mathematical Reviews

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, etc. I also attempted to approach Kurt Gödel’s great work on undecidability, helped and guided by my friend Karl Menger. At the same time Abraham Wald, to whom I had been able to offer a position as statistician in my Institute, gave me special instruction in various fields of mathematics. In

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paper anywhere, certainly in an economic periodical or book. Incidentally, in my paper there is also a strong reference to the fundamental work done by Abraham Wald (also in the 1930’s at Menger’s Colloquium) on the Walrasian system, a work again not taken up by Hicks, Johnny read my paper

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appeared two very fine expositions of our efforts by Leonid Hurwicz [4, 1945] and Jacob Marschak [6, 1946] as well as a long review by Abraham Wald [24, 1947], who in 1945 had already laid a new theory of the foundations of statistical estimation based on the theory of the zero-sum

The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant From Two Centuries of Controversy

by Sharon Bertsch McGrayne · 16 May 2011 · 561pp · 120,899 words

to the next box. This almost halved the number of tests required, and the use of logarithms massively simplified calculations by substituting addition for multiplication. Abraham Wald of Columbia University is generally credited with discovering sequential analysis for testing ammunition in the United States later during the war. But Good concluded that

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realizing how radically I was behaving. That was the natural thing to do. No big deal.”11 When Raiffa gave a series of seminars on Abraham Wald’s new book Statistical Decision Functions, he discovered it was full of Bayesian decisionmaking rules for use in a frequentist framework. Independently of Turing and

The Art of Computer Programming

by Donald Ervin Knuth · 15 Jan 2001

if Un < p or by 0 if Un > p, for a given probability p. Thus Copeland was essentially suggesting a return to Definition Rl. Then Abraham Wald showed that it is not necessary to weaken von Mises's definition so drastically, and he proposed substituting a countable set of subsequence rules. In

Nobody's Fool: Why We Get Taken in and What We Can Do About It

by Daniel Simons and Christopher Chabris · 10 Jul 2023 · 338pp · 104,815 words

, then the army could fix the vulnerable sections, strengthen the planes, and possibly end the war sooner. To help with this problem, the army found Abraham Wald, a Romanian-born statistician working with the Statistical Research Group at Columbia University. Wald’s work remains influential, with some of the statistical techniques he

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York: Penguin, 2014). The details of the Wald story, along with the iconic plane image, are described well in the Wikipedia article “Abraham Wald” [https://en.wikipedia.org/wiki/Abraham_Wald]; details about Black Thursday can also be found at “Boeing B-17 Flying Fortress,” Wikipedia [https://en.wikipedia.org/wiki/Boeing_B-17

The Data Detective: Ten Easy Rules to Make Sense of Statistics

by Tim Harford · 2 Feb 2021 · 428pp · 103,544 words

stages of the pandemic, when the most difficult policy decisions were being made, systematic testing was elusive. There’s a famous story about the mathematician Abraham Wald, who was asked in 1943 to advise the US Air Force on how to reinforce its planes. The planes were returning from sorties peppered with

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are.5 The rabbit hole goes deeper. Even the story about survivorship bias is an example of survivorship bias; it bears little resemblance to what Abraham Wald actually did, which was to produce a research document full of complex technical analysis. That is largely forgotten. What survives is the tale about a

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. 5. The story is well told in Jordan Ellenberg’s book How Not to Be Wrong (New York: Penguin, 2014), with the relevant extract here: “Abraham Wald and the Missing Bullet Holes,” Medium, July 14, 2016, https://medium.com/@penguinpress/an-excerpt-from-how-not-to-be-wrong-by-jordan-ellenberg-664e708cfc3d

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. 6. A technical summary (along with some grumbling about how the story has been exaggerated) is in Bill Casselman, “The Legend of Abraham Wald,” American Mathematical Society, http://www.ams.org/publicoutreach/feature-column/fc-2016-06. 7. An excellent account of the controversy is Daniel Engber, “Daryl Bem