All models are wrong
Quotations of George Box
Since all models are wrong the scientist cannot obtain a "correct" one by excessive elaboration. On the contrary following William of Occam he should seek an economical description of natural phenomena. Just as the ability to devise simple but evocative models is the signature of the great scientist so overelaboration and overparameterization is often the mark of mediocrity.
Box repeated the aphorism in a paper that was published in the proceedings of a 1978 statistics workshop. The paper contains a section entitled "All models are wrong but some are useful". The section is copied below.
Now it would be very remarkable if any system existing in the real world could be exactly represented by any simple model. However, cunningly chosen parsimonious models often do provide remarkably useful approximations. For example, the law PV = RT relating pressure P, volume V and temperature T of an "ideal" gas via a constant R is not exactly true for any real gas, but it frequently provides a useful approximation and furthermore its structure is informative since it springs from a physical view of the behavior of gas molecules.
For such a model there is no need to ask the question "Is the model true?". If "truth" is to be the "whole truth" the answer must be "No". The only question of interest is "Is the model illuminating and useful?".
Box repeated the aphorism twice more in his 1987 book, Empirical Model-Building and Response Surfaces (which was co-authored with Norman Draper). The first repetition is on p. 74: "Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful." The second repetition is on p. 424: "Essentially, all models are wrong, but some are useful".
Box's widely cited book Statistics for Experimenters (co-authored with William Hunter) does not include the aphorism in its first edition (published in 1978). The second edition (published in 2005; co-authored with William Hunter and J. Stuart Hunter) includes the aphorism three times: on p. 208, p. 384, and p. 440. On p. 440, the relevant sentence is this: "The most that can be expected from any model is that it can supply a useful approximation to reality: All models are wrong; some models are useful".
Comments and discussions
... it does not seem helpful just to say that all models are wrong. The very word model implies simplification and idealization. The idea that complex physical, biological or sociological systems can be exactly described by a few formulae is patently absurd. The construction of idealized representations that capture important stable aspects of such systems is, however, a vital part of general scientific analysis and statistical models, especially substantive ones, do not seem essentially different from other kinds of model.
A model is a simplification or approximation of reality and hence will not reflect all of reality. ... Box noted that “all models are wrong, but some are useful.” While a model can never be “truth,” a model might be ranked from very useful, to useful, to somewhat useful to, finally, essentially useless.
If I say that a map is wrong, it means that a building is misnamed, or the direction of a one-way street is mislabeled. I never expected my map to recreate all of physical reality, and I only feel ripped off if my map does not correctly answer the questions that it claims to answer. My maps of Philadelphia are useful. Moreover, except for a few that are out-of-date, they are not wrong.
I take his general point, which is that a street map could be exactly correct, to the resolution of the map.
... The saying, “all models are wrong,” is helpful because it is not completely obvious....
This is a simple point, and I can see how Steele can be irritated by people making a big point about it. But, the trouble is, many people don’t realize that all models are wrong.
In general, when building statistical models, we must not forget that the aim is to understand something about the real world. Or predict, choose an action, make a decision, summarize evidence, and so on, but always about the real world, not an abstract mathematical world: our models are not the reality—a point well made by George Box in his oft-cited remark that “all models are wrong, but some are useful”.
Additionally, the aphorism has been recommended to be a core part of the Applied Statistician's Creed.
This section needs expansion. You can help by adding to it. (January 2015)
… no models are [true]—not even the Newtonian laws. When you construct a model you leave out all the details which you, with the knowledge at your disposal, consider inessential…. Models should not be true, but it is important that they are applicable, and whether they are applicable for any given purpose must of course be investigated. This also means that a model is never accepted finally, only on trial.
- Box, G. E. P. (1976), "Science and Statistics" (PDF), Journal of the American Statistical Association, 71: 791–799, doi:10.1080/01621459.1976.10480949.
- Box, G. E. P. (1979), "Robustness in the strategy of scientific model building", in Launer, R. L.; Wilkinson, G. N., Robustness in Statistics, Academic Press, pp. 201–236.
- Box, G. E. P.; Draper, N. R. (1987), Empirical Model-Building and Response Surfaces, John Wiley & Sons.
- Box, G. E. P.; Hunter, W. G. (1978), Statistics for Experimenters, John Wiley & Sons.
- Box, G. E. P.; Hunter, J. S.; Hunter, W. G. (2005), Statistics for Experimenters (2nd ed.), John Wiley & Sons.
- Cox, D. R. (1995), "Comment on “Model uncertainty, data mining and statistical inference”", Journal of the Royal Statistical Society, Series A, 158: 455–456.
- Burnham, K. P.; Anderson, D. R. (2002), Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach (2nd ed.), Springer-Verlag, ISBN 0-387-95364-7. [This has over 41000 citations on Google Scholar.]
- Steele, J. M., "Models: Masterpieces and Lame Excuses".
- Gelman, A. (12 June 2008), "Some thoughts on the saying, “All models are wrong, but some are useful”".
- Hand, D. J. (2014), "Wonderful examples, but let's not close our eyes", Statistical Science, 29: 98–100, arXiv: , doi:10.1214/13-STS446.
- Wit, E.; van den Heuvel, E.; Romeijn, J.-W. (2012), "'All models are wrong...': an introduction to model uncertainty" (PDF), Statistica Neerlandica, 66: 217–236, doi:10.1111/j.1467-9574.2012.00530.x. [See too the workshop web page: "All models are wrong...".]
- Nester, M. R. (1996), "An applied statistician's creed" (PDF), Journal of the Royal Statistical Society, Series C, 45: 401–410, doi:10.2307/2986064.
- Rasch, G. (1960), Probabilistic Models for Some Intelligence and Attainment Tests, Copenhagen: Danmarks Paedogogiske Institut, pp. 37–38; republished by University of Chicago Press, 1980.
- von Neumann, J. (1947), "The Mathematician", in Haywood, R. B., Works of the Mind, University of Chicago Press, pp. 180–196.
- Anderson, C. (23 June 2008), "The end of theory", Wired.
- Lavine, M. et al. (May 2015), "In Response to ‘Statistics as a Science, Not an Art: The Way to Survive in Data Science’ by Mark van der Laan", Amstat News (magazine of the American Statistical Association).
- Saltelli, A.; Funtowicz, S. (2014), "When all models are wrong", Issues in Science and Technology, 30.
- “All Models are Right, Most are Useless” —Andrew Gelman blog
- Are all models wrong? —Theory, Evolution, and Games blog
- What is the meaning of “All models are wrong, but some are useful” —Stack Exchange