All models are wrong

"All models are wrong" is a common aphorism and anapodoton 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.

History

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The phrase "all models are wrong" was attributed to George Box who used the phrase in a 1976 paper 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.{{Citation |last=Box |first=George E. P. |title=Science and statistics |journal=Journal of the American Statistical Association |volume=71 |issue=356 |pages=791–799 |year=1976 |url=http://www-sop.inria.fr/members/Ian.Jermyn/philosophy/writings/Boxonmaths.pdf |doi=10.1080/01621459.1976.10480949}}.{{rp|792}} 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.{{Citation |author1-last=McCullagh |author1-first=P. |title=Generalized Linear Models |year=1983 |at=§1.1.4 |publisher=Chapman & Hall |author2-last=Nelder |author2-first=J. A.}}.{{Citation |author1-last=McCullagh |author1-first=P. |title=Generalized Linear Models |year=1989 |at=§1.1.4 |edition=second |publisher=Chapman & Hall |author2-last=Nelder |author2-first=J. A.}}. In 1996, an Applied Statistician's Creed was proposed by M.R. Nester, which incorporated the aphorism as a central tenet.{{Citation |last=Nester |first=M. R. |title=An applied statistician's creed |journal=Journal of the Royal Statistical Society, Series C |volume=45 |issue=4 |pages=401–410 |year=1996 |url=http://www.sortie-nd.org/lme/Statistical%20Papers/Nester_1996.pdf |doi=10.2307/2986064 |jstor=2986064}}.

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."{{Cite book |last=Korzybski |first=Alfred |title=Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics |date=1933 |publisher=International Non-Aristotelian Library Publishing Company / Science Press Printing Company |edition=1st |location=Lancaster, PA}} 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.The relatedness of Shewhart's quotation with the aphorism "all models are wrong" is noted by {{Harvtxt|Fricker|Woodall|2016}}. John von Neumann, in 1947, remarked that "truth is much too complicated to allow anything but approximations."

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.{{Citation |last=Box |first=G. E. P. |title=Robustness in Statistics |pages=201–236 |year=1979 |editor1-last=Launer |editor1-first=R. L. |url=https://archive.org/details/robustnessinstat0000unse/page/n1/mode/2up |contribution=Robustness in the strategy of scientific model building |publisher=Academic Press |doi=10.1016/B978-0-12-438150-6.50018-2 |isbn=978-1-4832-6336-6 |editor2-last=Wilkinson |editor2-first=G. N.}} 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.{{Citation |last1=Box |first1=G. E. P. |title=Empirical Model-Building and Response Surfaces |year=1987 |publisher=John Wiley & Sons |last2=Draper |first2=N. R.}}.

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.{{Citation | last=Cox | first= D. R. | year= 1995 | title= Comment on "Model uncertainty, data mining and statistical inference" | journal= Journal of the Royal Statistical Society, Series A | volume= 158 | pages=455–456}}.

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.{{Citation |last1=Burnham |first1=K. P. |last2=Anderson |first2=D. R. |year=2002 |title=Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach |edition=2nd |publisher= Springer-Verlag | at= §1.2.5}}.

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.Steele, J. M., "[http://www-stat.wharton.upenn.edu/~steele/Rants/ModelsMandLE.html Models: Masterpieces and Lame Excuses]". 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.Gelman, A. (12 June 2008), "[http://andrewgelman.com/2008/06/12/all_models_are/ Some thoughts on the saying, 'All models are wrong, but some are useful']".

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.{{citation| last=Truran | first= P. | chapter= Models: Useful but Not True | year= 2013 | title= Practical Applications of the Philosophy of Science | publisher= Springer | pages= 61–67 | doi=10.1007/978-3-319-00452-5_10 | series= SpringerBriefs in Philosophy | isbn= 978-3-319-00451-8 }}.

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.{{Citation | last= Hand | first= D. J. | title= Wonderful examples, but let's not close our eyes | journal= Statistical Science | year= 2014 | volume= 29 | pages= 98–100 | doi= 10.1214/13-STS446 | arxiv= 1405.4986 | doi-access= free }}.

Notes

References

{{Citation| author-first= N. | author-last= Ashby | author-link= Neil Ashby | title= Relativity and the Global Positioning System | journal= Physics Today | year= 2002 | volume= 55 | issue= 5 | pages= 41–47 | url= http://webs.ftmc.uam.es/juancarlos.cuevas/Teaching/GPS_relativity.pdf | doi=10.1063/1.1485583| bibcode= 2002PhT....55e..41A }}.
{{Citation |author1-last= Fricker | author1-first= R. D., Jr. | author2-last= Woodall | author2-first= W. H. | date= 2016 | journal= Significance | title= Play it again, and again, Sam |volume= 13 | issue= 4| page= 46 | doi= 10.1111/j.1740-9713.2016.00944.x | doi-access= free }}.
{{Citation|title=Collected Works of Paul Valéry, Volume 14—Analects|last=Valéry|first=Paul|publisher=Princeton University Press|year=1970 | translator= Stuart Gilbert}}.
{{Citation| first= J. L. | last= Vankat | title= Vegetation Dynamics on the Mountains and Plateaus of the American Southwest | year= 2013 | publisher= Springer}}.
{{Citation| first1= M. C. | last1= Wolfson | first2= B. B. | last2= Murphy | title= New views on inequality trends | journal= Monthly Labor Review | date= April 1998 | pages= 3–23 | url= https://www.bls.gov/opub/mlr/1998/04/art1full.pdf }}.

External links

[http://andrewgelman.com/2012/03/04/all-models-are-right-most-are-useless/ "All Models are Right, Most are Useless"]—Andrew Gelman blog
[https://telescoper.wordpress.com/2013/05/17/all-models-are-wrong/ All models are wrong]—Peter Coles blog

Category:Aphorisms

Category:Quotations from science

Category:1976 quotations

Category:Statistical models