Wednesday, December 31, 2014

Econometricians' Debt to Alan Turing

The other day, Carol and I went with friends to see the movie, The Imitation Game. I definitely recommend it.

I was previously aware of many of Alan Turing's contributions, especially in relation to the Turing Machine, cryptography, computing, and artificial intelligence. However, I hadn't realized the extent of Turing's use of, and contributions to, a range of important statistical tools. Some of these tools have a direct bearing on Econometrics.

For example:
  • (HT to Lief Bluck for this one.) In 1935, at the tender age of 22, Turing was appointed a Fellow at King's College, Cambridge, on the basis of his 1934 (undergraduate) thesis in which he proved the Central Limit Theorem. More specifically, he derived a proof of what we now call the Lindeberg-Lévy Central Limit Theorem.  He was not aware of Lindeberg's earlier work (1920-1922) on this problem. Lindeberg, in turn, was unaware of Lyapunov's earlier results. (Hint: there was no internet back then!). How many times has your econometrics instructor waved her/his arms and muttered " a result of the central limit theorem....."?
  • In 1939, Turing developed what Wald and his collaborators would later call "sequential analysis". Yes, that's Abraham Wald who's associated with the Wald tests that you use all of the time.Turing's wartime work on this subject remained classified until the 1980's. Wald's work became well-established in the literature by the late 1940's, and was included in the statistics courses that I took as a student in the 1960's. Did I mention that Wald's wartime associates included some familiar names from economics? Namely, Trygve Haavelmo, Harold Hotelling, Jacob Marschak, Milton Friedman, W. Allen Wallis, and Kenneth Arrow.
  • The mathematician/statistician I. J. ("Jack") Good was a member of Turing's team at Bletchley Park that cracked the Enigma code. Good was hugely influential in the development of modern Bayesian methods, many of which have found their way into econometrics. He described the use of Bayesian inference in the Enigma project in his "conversation" with Banks (1996). (This work also gave us the Good-Turing estimator - e.g., see Good, 1953.)
  • Turing (1948) devised the LU ("Lower and Upper") Decomposition that is widely used for matrix inversion and for solving systems of linear equations. Just think how many times you invert matrices when you're doing your econometrics, and how important it is that the calculations are both fast and accurate!
Added, 20 February, 2015: I have recently become aware of Good (1979)


Banks, D. L., 1996. A conversation with I. J. Good. Statistical Science, 11, 1-19.

Good, I. J., 1953.The population frequencies of species and the estimation of population parameters. Biometrika, 40, 237-264.

Good, I. J., 1979. A. M. Turing's statistical work in World War II. Biometrika, 66, 393-396.

Turing, A. M., 1948. Rounding-off errors in matrix processes. Quarterly Journal of Mechanics and Applied Mathematics, 1, 287-308.

© 2014, David E. Giles