abraham waldFrom Wikipedia: Abraham Wald (October 31, 1902 - December 13, 1950) was a mathematician born in Cluj, in the then Austria–Hungary (present-day Romania) who contributed to decision theory, geometry, and econometrics, and founded the field of statistical sequential analysis.

And here is a very nice paper on Wald's work during WWII:

Abraham Wald's Work on Aircraft Survivability Marc Mangel, Francisco J. Samaniego Journal of the American Statistical Association, Vol 79, Issue 386 (June, 1984)

The paper is an excellent bit of homework for those in the Counting 101 class, who also enjoy their history. One is forced to take out pencil and paper, but it's worth the effort.

Wald analyzed data on bombers returning from missions over the Continent. One objective was to determine what parts of the aircraft might be strengthened in order to reduce losses. The paper lays out the following case: Divide the surface area of a bomber into four parts and determine what percentage of total surface area each of the four parts represents:

aircraft surface area:

engine 26.9%

fuselage 34.6%

fuel system 15.4%

everything else 23.1%

Then examine the 380 aircraft that returned from a mission on which 400 were sent. Count the number of hits in each of the four areas and calculate what percentage of total hits this represents:

hit distribution:

engine 18.6%

fuselage 38.2%

fuel system 17.7%

everything else 25.5%

Doing a simple comparison between surface area and hit distribution gives the following over/under:

hit_distribution_% minus surface_area_%: engine -8.3% fuselage +3.6% fuel system +2.3% everything else +2.4%

It appears the engines are getting hit less often than expected, and the fuselage more, so we should strengthen the fuselage. But of course, we are leaving something out, and it's very interesting to work through Wald's analysis (at an introductory level, certainly) and see the results.

Bill Egan adds:

Go read Wald's book Sequential Analysis . Wonderful work; published 3 years before his untimely death. I have been working in that area and after reading Wald's book, I delved into all the work done afterwards. Surprisingly little progress, and after reading 20+ papers, I have thrown my hands up in the air. Lots of screaming pygmies flinging pygmy pellets at each other and at the dead giant Wald.  


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