You’ve all seen those bulls-eye pictures representing bias and variance (see for example the wikipedia page). Where did this come from? I’m writing an article where I want to cite the idea and I’m not sure where to look. It’s a pretty natural idea but it must come from somewhere, right?
That comes up in discussions of accuracy and precision by analogy to archery/games with a target. Maybe it came from there?
Yes, but where, exactly?
It seems my answer was accurate but not precise.
I remember these on the wall of Mr McCarthy’s science class in 8th grade. Does that count as a source?
The ChatGPT bot says, “The origins of this diagram are not well-known.” 😂
Goddam magic 8 ball.
I’ve seen early examples of those ideas in training documents for naval fire control, and the practical use was interpreting the splashes of near misses (e.g. accurate for range but not for line, and vice-verse) along with more general idea of concentration of fire.
Might be worth trying to find the origins of the bias-variance (tradeoff?) concept and then looking to see how they represented it.
Google Ngram Viewer dates the first recorded occurrence of term “bias-variance” to 1956, and Page 3 of 1955’s “Fishery Investigations”
by the Great Britain Ministry of Agriculture does write: “The ‘best’ estimates will be those which, in statistical terms, are unbiased and of minimum variance. These terms may be explained most easily by comparison with a gun shooting at a target . If the gun is biased the shots will all…” and so on,
I also asked ChatGPT, which said “The concept of the bias-variance tradeoff was first introduced by G. D. Forney Jr. in the 1960s.”
Usually I see this the target cartoon as illustrating the difference between the (obviously related) related terms “accuracy” and “precision”, though — bias and variance more often get a high and low (0th) order polynomial fit to a scatterplot.
Nikolai, can you link to an example of the polynomial fit representations that you mention please?
Sure — just looking at the first row of google image search results for <>, something like the 3rd and 6th hits: https://i.imgur.com/ch6KWnZ.png
(ofc, the 1st, 4th, and 5th are all the target illustration! So maybe my own experiences are not representative. I think I’ve only ever seen them introduced in the context of intro to linear regression, though, which might underlie my biased but precise claim :S)
Googling a bit, here’s this 1996 Travel Survey Manual that cites this as the bullseye source: “Survey Methods for Transport Planning” (1995). So, at least 1995.
Hi Raghu, well spotted! I originally developed this idea (without reference to previous works) in 1979 when preparing a set of notes for a course on Travel Survey Methods at Monash University, Melbourne, Australia. It was then incorporated in the Course Notes which were published in 1982 (Richardson, A.J. (1982). Transport Survey Methods, Monash University.). The analogy was then incorporated into the 1995 book that you reference. So, the reference goes back to at least 1982, but of course there may well be an earlier reference by someone else of which I am not aware.
Well I just scrolled through a pdf of Saracen archery: an English version and exposition of a Mameluke work on archery (ca. A.D. 1368), and didn’t see it there. So I guess sometime after the 14th century. Hope that narrows it down.
I’m going with George von Mayr:
https://datavis.ca/milestones/index.php?group=1850%2B&mid=ms151
Ostermann, Rüdiger. (1999). Georg von Mayrs Beiträge zur statistichen Graphik. Algemeines Statistiches Archiv. 83. 3. 350-362
These diagrams are a regular feature across editions the Wildlife Society’s Wildlife Research and Management Techniques Manual. I have the 1996 (fifth) edition, which says modified from Overton & Davis (1969) and White et al. (1982).
OVERTON, W. S., and D. E. DAVIS. 1969. Estimating the numbers of animals in wildlife populations. Pages 403-456 in R. H. Giles, ed. Wildlife management techniques. Third ed. The Wildl. Soc., Washington DC
WHITE, G. C., D. R. ANDERSON, K. P. BURNHAM, and D. L. OTIS. 1982. Capture-recapture and removal methods for sampling closed populations. Rep. LA-8787-NERP, UC-11, Los Alamos Natl. Lab., Los Alamos, N.M. 235pp.
Dear Sir
I don’t think I have seen such a diagram until I followed the link you gave.
Yours Sincerely
very familiar to actuaries since 1981.
https://www.casact.org/abstract/examination-credibility-concepts
See references in
https://www.medicine.mcgill.ca/epidemiology/hanley/bios601/Likelihood/letter-jrssa-20110509.pdf
also
‘Stochastic’ https://www.allwords.com/word-stochastic.html French: stochas- tique(fr) German: stochastisch(de) Spanish: estocstico(es) Etymology: From Ancient Greek (polytonic, ), from (polytonic, ) “aim at a target, guess”, from (polytonic, ) “an aim, a guess”. Parzen, in his text on Stochastic Processes .. page 7 says: <<The word is of Greek origin; see Hagstroem (1940) for a study of the history of the word. In seventeenth century English, the word “stochastic” had the meaning “to conjecture, to aim at a mark.”
Not sure, but such bullseye pictures have also been used for ages to discuss reliability.