I'm trying to find a year of publication of the importance sampling technique. Does anyone has a reference on this?
I'm tempted to say 1970 (Hastings paper), but I would like to know if anyone knew this before.
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1$\begingroup$ This is so simple and natural that I would expect it to have been formalized by the 1930's but used, without naming it as such, by c. 1800. $\endgroup$– whuber ♦Commented Jun 4, 2022 at 11:53
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5 Answers
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Edit: Looks like sk1ll3r is correct that Kahn introduced the method a year earlier than this answer suggests. I haven't checked if the term "importance sampling" appears in the earlier references, though.
Original answer: It looks like the term was first proposed in
Kahn, H. and Harris, T. E. (1951). Estimation of particle transmission by random sampling. National Bureau of Standards applied mathematics series, 12:27–30.
https://dornsifecms.usc.edu/assets/sites/520/docs/kahnharris.pdf
Here's the relevant section (from the first column of the first page):
answered May 20, 2018 at 10:45
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I also found an article "Use of different Monte Carlo sampling techniques" from Herman Kahn, which is dated 30 November 1955 and which enumerates variance reduction techniques; Importance sampling is one of them. (https://www.rand.org/content/dam/rand/pubs/papers/2008/P766.pdf)
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One earlier reference is the Hammersley & Handscomb (1964) monograph on Monte Carlo methods (http://www.worldcat.org/title/monte-carlo-methods/oclc/312077), which details the technique on page 57 and following, naming it "importance sampling". This reference was used in a 1976 article by Siegmund (http://www.jstor.org/stable/2958179).
Unfortunately Hammersley & Handscomb do not give any reference for the method, so another earlier precedent, possibly a paper, might exist. You can find a PDF of this monograph quite easily, as it has been uploaded to several educational sites.
EDIT: Following Adela's answer, I found another reference: A Kahn and Marshall paper from 1953: http://www.jstor.org/stable/166789 ("Importance sampling" is explained from page 269 onwards). Again, the way its described suggests there is some earlier precedent.
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Art Owen attributes importance sampling to Kahn's papers from 1950 [1, 2] in Chapter 9's end notes of his Monte Carlo book [3].
[1] Herman Kahn. Random sampling (Monte Carlo) techniques in neutron attenuation problems, I. Nucleonics, 6(5):27–37, 1950a.
[2] Herman Kahn. Random sampling (Monte Carlo) techniques in neutron attenuation problems, II. Nucleonics, 6(6):60–65, 1950b.
[3] Art B. Owen. Monte Carlo theory, methods and examples. 2013.
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These 1949 references all contain mentions of importance sampling:
Goertzel, G. 1949 "Quota Sampling and Importance Functions in Stochastic Solution of Particle Problems." Technical Report ORNL-434, 21 June, 1949. Oak Ridge National Laboratory, Oak Ridge, TN.
Goertzel, G., and H. Kahn. 1949. "Monte Carlo Methods for Shield Computation." Technical Report ORNL-429, December 1949. Oak Ridge National Laboratory, Oak Ridge, TN.
Kahn, H. 1949. "Stochastic (Monte Carlo) Attenuation Analysis." Technical Report R-163, 14 June 1949. The Rand Corporation, Santa Monica, CA.
Kahn, H., and T. E. Harris. 1949 (?). "Estimation of Particle Transmission by Random Sampling." Proceedings of a Symposium Held June 29, 30, and July, 1, 1949, in Los Angeles, California, Under the Sponsorship of the Rand Corporation, and the National Bureau of Standards, with the Cooperation of the Oak Ridge National Laboratory later published in 1951 in Monte Carlo Method, Volume 12 of Applied Mathematics Series, 27--30: National Bureau of Standards.
