所有模型都是错的

“所有模型都是错的”（英语："All models are wrong"）是统计学中常见的格言，常引申为“所有模型都是错的，但有些是有用的”。它承认统计模型永远无法完全涵盖现实的复杂性，但仍能发挥实用价值。这句格言通常被认为出自英国统计学家乔治·E·P·博克斯，但其核心概念早于博克斯的著作便已存在。

历史

“所有模型都是错的”这句话被认为出自乔治·博克斯^[1]，他在1976年的一篇论文中借此形容模型的局限性，主张虽然没有任何模型能完全精准，但若审慎运用，较简单的模型仍能提供宝贵的洞见^[2]^:792。彼得·麦卡勒（Peter McCullagh）与约翰·内尔德（John Nelder）在1983年关于广义线性模型的著作中指出，尽管科学建模是创造性过程，某些模型仍优于其他模型，即便没有任何模型能宣称拥有永恒真理^[3]^[4]。1996年，M·R·内斯特（M. R. Nesterr）提出《应用统计学家的信条》，将此格言作为核心信条纳入其中^[1]。

尽管这句格言最常与乔治·博克斯联系在一起，但其核心思想在历史上已被多位思想家表达过。阿尔弗雷德·柯日布斯基早在1933年便指出：“地图并非其所代表的领土，但若绘制正确，它便与领土具有相似的结构，这正是其实用性的根源。”^[5]。1939年，沃特·安德鲁·休哈特论述了构建能完整描述统计控制状态之模型的不可行性，指出任何模型皆无法精确呈现此状态的特定特征^[6]。约翰·冯·诺伊曼于1947年曾指出：“真理过于复杂，只能容许近似值的存在。”^[2]

讨论

博克斯于1979年再次援引此格言，并进一步阐述其思想：尽管模型无法完美描述经验现象，却能作为实用的近似工具^[7]。他在后续著作中重申此观点，强调应依据模型的实用性而非绝对正确性来评断其价值^[8]^[6]。

戴维·科克斯在1995年的一篇评论中指出，宣称所有模型都是错误的并无助益，因为模型本质上就是对现实的简化。他强调，统计模型与其他科学模型一样，旨在透过理想化的表征来捕捉系统的重要面向^[9]。

在2002年关于统计模型选择的著作中，K·P·伯纳姆（K. P. Burnham）与D·R·安德森（D. R. Anderson）重申了博克斯的观点，指出尽管模型是对现实的简化，但其实用性存在显著差异——从极具价值到几乎毫无用处^[10]。

J·迈克尔·斯蒂尔（英语：J. Michael Steele）以城市地图为喻，阐释模型如同地图虽有局限却具实用价值，强调某些简化模型未必错误^[11]。安德鲁·葛尔曼（Andrew Gelman）回应时认同斯蒂尔观点，但仍力挺该格言的价值，特别是其能引导人们关注模型固有的缺陷^[12]。

哲学家彼得·特鲁兰（Peter Truran）在2013年的一篇论文中探讨了看似不相容的模型如何透过呈现同一现象的不同面向来做出精准预测，并以两名观察者从不同角度观看圆柱体的例子阐明此观点^[13]。

2014年，大卫·汉德（英语：David Hand (statistician)）重申模型旨在协助理解或决策现实世界，此观点亦为博克斯的名言所强调^[14]。

备注

^ ^1.0 ^1.1 Nester, M. R., An applied statistician's creed (PDF), Journal of the Royal Statistical Society, Series C, 1996, 45 (4): 401–410, JSTOR 2986064, doi:10.2307/2986064 .
^ ^2.0 ^2.1 Box, George E. P., Science and statistics (PDF), Journal of the American Statistical Association, 1976, 71 (356): 791–799, doi:10.1080/01621459.1976.10480949 .
^ McCullagh, P.; Nelder, J. A., Generalized Linear Models, Chapman & Hall, §1.1.4, 1983 .
^ McCullagh, P.; Nelder, J. A., Generalized Linear Models second, Chapman & Hall, §1.1.4, 1989 .
^ Korzybski, Alfred. Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics 1st. Lancaster, PA: International Non-Aristotelian Library Publishing Company / Science Press Printing Company. 1933.
^ ^6.0 ^6.1 The relatedness of Shewhart's quotation with the aphorism "all models are wrong" is noted by Fricker & Woodall (2016).
^ Box, G. E. P., Robustness in the strategy of scientific model building, Launer, R. L.; Wilkinson, G. N. (编), Robustness in Statistics, Academic Press: 201–236, 1979, ISBN 978-1-4832-6336-6, doi:10.1016/B978-0-12-438150-6.50018-2
^ Box, G. E. P.; Draper, N. R., Empirical Model-Building and Response Surfaces, John Wiley & Sons, 1987 .
^ Cox, D. R., Comment on "Model uncertainty, data mining and statistical inference", Journal of the Royal Statistical Society, Series A, 1995, 158: 455–456 .
^ Burnham, K. P.; Anderson, D. R., Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach 2nd, Springer-Verlag, §1.2.5, 2002 .
^ 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'".
^ Truran, P., Models: Useful but Not True, Practical Applications of the Philosophy of Science, SpringerBriefs in Philosophy, Springer: 61–67, 2013, ISBN 978-3-319-00451-8, doi:10.1007/978-3-319-00452-5_10 .
^ Hand, D. J., Wonderful examples, but let's not close our eyes, Statistical Science, 2014, 29: 98–100, arXiv:1405.4986 , doi:10.1214/13-STS446  .

参考资料

Ashby, N., Relativity and the Global Positioning System (PDF), Physics Today, 2002, 55 (5): 41–47, Bibcode:2002PhT....55e..41A, doi:10.1063/1.1485583 .
Fricker, R. D., Jr.; Woodall, W. H., Play it again, and again, Sam, Significance, 2016, 13 (4): 46, doi:10.1111/j.1740-9713.2016.00944.x  .
Valéry, Paul, Collected Works of Paul Valéry, Volume 14—Analects, 由Stuart Gilbert翻译, Princeton University Press, 1970 .
Vankat, J. L., Vegetation Dynamics on the Mountains and Plateaus of the American Southwest, Springer, 2013 .
Wolfson, M. C.; Murphy, B. B., New views on inequality trends (PDF), Monthly Labor Review, April 1998: 3–23 .

延伸阅读

Anderson, C. (23 June 2008), "The end of theory", Wired
Box, G. E. P., Statistics as a catalyst to learning by scientific method Part II—A discussion, Journal of Quality Technology, 1999, 31: 16–29, doi:10.1080/00224065.1999.11979890
Enderling, H.; Wolkenhauer, O., Are all models wrong?, Computational and Systems Oncology, 2021, 1 (1): e1008, PMC 7880041 , PMID 33585835, doi:10.1002/cso2.1008
Saltelli, A.; Funtowicz, S. (Winter 2014), "When all models are wrong", Issues in Science and Technology, 30

外部链接

"All Models are Right, Most are Useless"—Andrew Gelman blog
All models are wrong—Peter Coles blog

[Nester-1996-1] 1.0 ^1.1 Nester, M. R., An applied statistician's creed (PDF), Journal of the Royal Statistical Society, Series C, 1996, 45 (4): 401–410, JSTOR 2986064, doi:10.2307/2986064 .

[Box-1976-2] 2.0 ^2.1 Box, George E. P., Science and statistics (PDF), Journal of the American Statistical Association, 1976, 71 (356): 791–799, doi:10.1080/01621459.1976.10480949 .

[3] McCullagh, P.; Nelder, J. A., Generalized Linear Models, Chapman & Hall, §1.1.4, 1983 .

[4] McCullagh, P.; Nelder, J. A., Generalized Linear Models second, Chapman & Hall, §1.1.4, 1989 .

[5] Korzybski, Alfred. Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics 1st. Lancaster, PA: International Non-Aristotelian Library Publishing Company / Science Press Printing Company. 1933.

[ShewhartNote-6] 6.0 ^6.1 The relatedness of Shewhart's quotation with the aphorism "all models are wrong" is noted by Fricker & Woodall (2016).

[7] Box, G. E. P., Robustness in the strategy of scientific model building, Launer, R. L.; Wilkinson, G. N. (编), Robustness in Statistics, Academic Press: 201–236, 1979, ISBN 978-1-4832-6336-6, doi:10.1016/B978-0-12-438150-6.50018-2

[8] Box, G. E. P.; Draper, N. R., Empirical Model-Building and Response Surfaces, John Wiley & Sons, 1987 .

[9] Cox, D. R., Comment on "Model uncertainty, data mining and statistical inference", Journal of the Royal Statistical Society, Series A, 1995, 158: 455–456 .

[10] Burnham, K. P.; Anderson, D. R., Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach 2nd, Springer-Verlag, §1.2.5, 2002 .

[11] Steele, J. M., "Models: Masterpieces and Lame Excuses".

[12] Gelman, A. (12 June 2008), "Some thoughts on the saying, 'All models are wrong, but some are useful'".

[13] Truran, P., Models: Useful but Not True, Practical Applications of the Philosophy of Science, SpringerBriefs in Philosophy, Springer: 61–67, 2013, ISBN 978-3-319-00451-8, doi:10.1007/978-3-319-00452-5_10 .

[14] Hand, D. J., Wonderful examples, but let's not close our eyes, Statistical Science, 2014, 29: 98–100, arXiv:1405.4986 , doi:10.1214/13-STS446  .

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