所有模型都是錯的

「所有模型都是錯的」（英語："All models are wrong"）是統計學中常見的格言，常引申為「所有模型都是錯的，但有些是有用的」。它承認統計模型永遠無法完全涵蓋現實的複雜性，但仍能發揮實用價值。這句格言通常被認為出自英國統計學家喬治·E·P·博克斯，但其核心概念早於博克斯的著作便已存在。

歷史

「所有模型都是錯的」這句話被認為出自喬治·博克斯^[1]，他在1976年的一篇論文中藉此形容模型的局限性，主張雖然沒有任何模型能完全精準，但若審慎運用，較簡單的模型仍能提供寶貴的洞見^[2]^:792。彼得·麥卡勒（Peter McCullagh）與約翰·內爾德（John Nelder）在1983年關於廣義線性模型的著作中指出，儘管科學建模是創造性過程，某些模型仍優於其他模型，即便沒有任何模型能宣稱擁有永恆真理^[3]^[4]。1996年，M·R·內斯特（M. R. Nesterr）提出《應用統計學家的信條》，將此格言作為核心信條納入其中^[1]。

儘管這句格言最常與喬治·博克斯聯繫在一起，但其核心思想在歷史上已被多位思想家表達過。阿爾弗雷德·柯日布斯基早在1933年便指出：「地圖並非其所代表的領土，但若繪製正確，它便與領土具有相似的結構，這正是其實用性的根源。」^[5]。1939年，沃特·安德魯·休哈特論述了構建能完整描述統計控制狀態之模型的不可行性，指出任何模型皆無法精確呈現此狀態的特定特徵^[6]。約翰·馮·諾伊曼於1947年曾指出：「真理過於複雜，只能容許近似值的存在。」^[2]

討論

博克斯於1979年再次援引此格言，並進一步闡述其思想：儘管模型無法完美描述經驗現象，卻能作為實用的近似工具^[7]。他在後續著作中重申此觀點，強調應依據模型的實用性而非絕對正確性來評斷其價值^[8]^[6]。

戴維·科克斯在1995年的一篇評論中指出，宣稱所有模型都是錯誤的並無助益，因為模型本質上就是對現實的簡化。他強調，統計模型與其他科學模型一樣，旨在透過理想化的表徵來捕捉系統的重要面向^[9]。

在2002年關於統計模型選擇的著作中，K·P·伯納姆（K. P. Burnham）與D·R·安德森（D. R. Anderson）重申了博克斯的觀點，指出儘管模型是對現實的簡化，但其實用性存在顯著差異——從極具價值到幾乎毫無用處^[10]。

J·邁克爾·斯蒂爾（英语：J. Michael Steele）以城市地圖為喻，闡釋模型如同地圖雖有局限卻具實用價值，強調某些簡化模型未必錯誤^[11]。安德魯·葛爾曼（Andrew Gelman）回應時認同斯蒂爾觀點，但仍力挺該格言的價值，特別是其能引導人們關注模型固有的缺陷^[12]。

哲學家彼得·特魯蘭（Peter Truran）在2013年的一篇論文中探討了看似不相容的模型如何透過呈現同一現象的不同面向來做出精準預測，並以兩名觀察者從不同角度觀看圓柱體的例子闡明此觀點^[13]。

2014年，大衛·漢德（英语：David Hand (statistician)）重申模型旨在協助理解或決策現實世界，此觀點亦為博克斯的名言所強調^[14]。

備註

^ ^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  .

參考資料

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 .

延伸閱讀

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

外部連結

"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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