All models are wrong

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"All models are wrong" is a common aphorism in statistics. It is often expanded as "All models are wrong, but some are useful". The aphorism acknowledges that statistical models always fall short of the complexities of reality but can still be useful nonetheless. The aphorism is generally attributed to George E. P. Box, a British statistician, although the underlying concept predates Box's writings.

Contents

History

The phrase is attributed to George Box GeorgeEPBox (cropped).jpg
The phrase is attributed to George Box

The first part of the quote ("All models are wrong") appeared as early as 1976in one of Box's papers [1] to refer to the limitations of models, arguing that while no model is ever completely accurate, simpler models can still provide valuable insights if applied judiciously. The full quote appears on p. 424 of Box and Draper (1987, Empirical Model-Building and Response Surfaces) [2] . In the section "The Use of Approximating Functions," Box and Draper use a polynomial to approximate a true response function. They write:

"The fact that the polynomial is an approximation does not necessarily detract from its usefulness because all models are approximations, Essentially, all models are wrong, but some are useful."

In their 1983 book on generalized linear models, Peter McCullagh and John Nelder stated that while modeling in science is a creative process, some models are better than others, even though none can claim eternal truth. [3] [4] In 1996, an Applied Statistician's Creed was proposed by M.R. Nester, which incorporated the aphorism as a central tenet. [5]

Although the aphorism is most commonly associated with George Box, the underlying idea has been historically expressed by various thinkers in the past. Alfred Korzybski noted in 1933, "A map is not the territory it represents, but, if correct, it has a similar structure to the territory, which accounts for its usefulness." [6] In 1939, Walter Shewhart discussed the impossibility of constructing a model that fully characterizes a state of statistical control, noting that no model can exactly represent any specific characteristic of such a state. [7] John von Neumann, in 1947, remarked that "truth is much too complicated to allow anything but approximations." [1] Another similar sentiment is expressed by the Goodhart's law attributed to British economist Charles Goodhart . It's an adage that has been stated as, "When a measure becomes a target, it ceases to be a good measure". The core idea of the adage was expressed in a 1975 article on monetary policy in the United Kingdom [8] .

Discussions

Box used the aphorism again in 1979, where he expanded on the idea by discussing how models serve as useful approximations, despite failing to perfectly describe empirical phenomena. [9] He reiterated this sentiment in his later works, where he discussed how models should be judged based on their utility rather than their absolute correctness. [10] [7]

David Cox, in a 1995 commentary, argued that stating all models are wrong is unhelpful, as models by their nature simplify reality. He emphasized that statistical models, like other scientific models, aim to capture important aspects of systems through idealized representations. [11]

In their 2002 book on statistical model selection, Burnham and Anderson reiterated Box's statement, noting that while models are simplifications of reality, they vary in usefulness, from highly useful to essentially useless. [12]

J. Michael Steele used the analogy of city maps to explain that models, like maps, serve practical purposes despite their limitations, emphasizing that certain models, though simplified, are not necessarily wrong. [13] In response, Andrew Gelman acknowledged Steele's point but defended the usefulness of the aphorism, particularly in drawing attention to the inherent imperfections of models. [14]

Philosopher Peter Truran, in a 2013 essay, discussed how seemingly incompatible models can make accurate predictions by representing different aspects of the same phenomenon, illustrating the point with an example of two observers viewing a cylindrical object from different angles. [15]

In 2014, David Hand reiterated that models are meant to aid in understanding or decision-making about the real world, a point emphasized by Box's famous remark. [16]

See also

Notes

  1. 1 2 Box, George E. P. (1976), "Science and statistics" (PDF), Journal of the American Statistical Association , 71 (356): 791–799, doi:10.1080/01621459.1976.10480949 .
  2. ↑ Box, George E. P. Empirical Model-Building and Response Surfaces /. New York : Wiley,. Print. p. 424.
  3. ↑ McCullagh, P.; Nelder, J. A. (1983), Generalized Linear Models, Chapman & Hall, §1.1.4.
  4. ↑ McCullagh, P.; Nelder, J. A. (1989), Generalized Linear Models (second ed.), Chapman & Hall, §1.1.4.
  5. ↑ Nester, M. R. (1996), "An applied statistician's creed" (PDF), Journal of the Royal Statistical Society, Series C , 45 (4): 401–410, doi:10.2307/2986064, JSTOR   2986064 .
  6. ↑ Korzybski, Alfred (1933). Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics (1st ed.). Lancaster, PA: International Non-Aristotelian Library Publishing Company / Science Press Printing Company.
  7. 1 2 The relatedness of Shewhart's quotation with the aphorism "all models are wrong" is noted by Fricker & Woodall (2016).
  8. ↑ Goodhart, Charles (1975). "Problems of Monetary Management: The UK Experience". Papers in Monetary Economics. Papers in monetary economics 1975; 1; 1. - [Sydney]. - 1975, p. 1-20. Vol. 1. Sydney: Reserve Bank of Australia.
  9. ↑ Box, G. E. P. (1979), "Robustness in the strategy of scientific model building", in Launer, R. L.; Wilkinson, G. N. (eds.), Robustness in Statistics, Academic Press, pp. 201–236, doi:10.1016/B978-0-12-438150-6.50018-2, ISBN   978-1-4832-6336-6
  10. ↑ Box, G. E. P.; Draper, N. R. (1987), Empirical Model-Building and Response Surfaces, John Wiley & Sons .
  11. ↑ Cox, D. R. (1995), "Comment on "Model uncertainty, data mining and statistical inference"", Journal of the Royal Statistical Society, Series A , 158: 455–456.
  12. ↑ Burnham, K. P.; Anderson, D. R. (2002), Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach (2nd ed.), Springer-Verlag, §1.2.5.
  13. ↑ Steele, J. M., "Models: Masterpieces and Lame Excuses".
  14. ↑ Gelman, A. (12 June 2008), "Some thoughts on the saying, 'All models are wrong, but some are useful'".
  15. ↑ Truran, P. (2013), "Models: Useful but Not True", Practical Applications of the Philosophy of Science, SpringerBriefs in Philosophy, Springer, pp. 61–67, doi:10.1007/978-3-319-00452-5_10, ISBN   978-3-319-00451-8 .
  16. ↑ Hand, D. J. (2014), "Wonderful examples, but let's not close our eyes", Statistical Science , 29: 98–100, arXiv: 1405.4986 , doi: 10.1214/13-STS446 .

References

Further reading

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