推論統計學

安德森鳶尾花卉數據集中變色鳶尾花萼片寬度數據的分佈直方圖

推論統計學，或稱統計推論（英語：Statistical inference），指統計學中，研究如何根據樣本數據去推斷總體數量特徵的方法。它是在對樣本數據進行描述的基礎上，對統計總體的未知數量特徵做出以概率形式表述的推斷。更概括地說，是在一段有限的時間內，通過對一個隨機過程的觀察來進行推斷的。

統計學中，統計推論與敘述統計相對應。

統計推論的結果常用來決定下一步的作法，可能是要做更深入的試驗或問卷，或是是決定是否要實行某項方案。

參考文獻

• Bandyopadhyay, P. S.; Forster, M. R. (編), Philosophy of Statistics, Elsevier, 2011 .
• Bickel, Peter J.; Doksum, Kjell A. Mathematical statistics: Basic and selected topics 1 Second (updated printing 2007). Prentice Hall. 2001. ISBN 0-13-850363-X. MR 0443141. 
• Cox, D. R. (2006). Principles of Statistical Inference, Cambridge University Press. ISBN 0-521-68567-2.
• Fisher, R. A. (1955), "Statistical methods and scientific induction", Journal of the Royal Statistical Society, Series B, 17, 69—78. (criticism of statistical theories of Jerzy Neyman and 沃德·亞伯拉罕)
• Freedman, D. A. Statistical Models: Theory and practice revised. Cambridge University Press. 2009: xiv+442 pp. ISBN 978-0-521-74385-3. MR 2489600. 
• Freedman, D. A. (2010). Statistical Models and Causal Inferences: A Dialogue with the Social Sciences (Edited by David Collier, Jasjeet S. Sekhon, and Philip B. Stark), Cambridge University Press.
• Hampel, Frank. The proper fiducial argument (PDF) (Research Report No. 114). Feb 2003 [29 March 2016]. （原始內容存檔 (PDF)於2017-05-10）. 
• Hansen, Mark H.; Yu, Bin. Model Selection and the Principle of Minimum Description Length: Review paper. Journal of the American Statistical Association. June 2001, 96 (454): 746–774. JSTOR 2670311. MR 1939352. doi:10.1198/016214501753168398. （原始內容存檔於2004-11-16）. 
• Hinkelmann, Klaus; Kempthorne, Oscar. Introduction to Experimental Design Second. Wiley. 2008. ISBN 978-0-471-72756-9. 
• Kolmogorov, Andrei N. On tables of random numbers. Sankhyā Ser. A. 1963, 25: 369–375. MR 0178484.  Reprinted as Kolmogorov, Andrei N. On tables of random numbers. Theoretical Computer Science. 1998, 207 (2): 387–395. MR 1643414. doi:10.1016/S0304-3975(98)00075-9. 
• Konishi S., Kitagawa G. (2008), Information Criteria and Statistical Modeling, Springer.
• Kruskal, William. Miracles and statistics: the casual assumption of independence (ASA Presidential Address). Journal of the American Statistical Association. December 1988, 83 (404): 929–940. JSTOR 2290117. doi:10.2307/2290117. 
• Le Cam, Lucian. (1986) Asymptotic Methods of Statistical Decision Theory, Springer. ISBN 0-387-96307-3
• Moore, D. S.; McCabe, G. P.; Craig, B. A. (2015), Introduction to the Practice of Statistics, Eighth Edition, Macmillan.
• Neyman, Jerzy. Note on an article by Sir Ronald Fisher. Journal of the Royal Statistical Society, Series B. 1956, 18 (2): 288–294. JSTOR 2983716.  (reply to Fisher 1955)
• Peirce, C. S. (1877–1878), "Illustrations of the logic of science" (series), Popular Science Monthly, vols. 12-13. Relevant individual papers:
  • (1878 March), "The Doctrine of Chances", Popular Science Monthly, v. 12, March issue, pp. 604 （頁面存檔備份，存於互聯網檔案館）–615. Internet Archive Eprint.
  • (1878 March), "The Doctrine of Chances", Popular Science Monthly, v. 12, March issue, pp. 604 （頁面存檔備份，存於互聯網檔案館）–615. Internet Archive Eprint.
  • (1878 June), "The Order of Nature", Popular Science Monthly, v. 13, pp. 203 （頁面存檔備份，存於互聯網檔案館）–217.Internet Archive Eprint.
  • (1878 August), "Deduction, Induction, and Hypothesis", Popular Science Monthly, v. 13, pp. 470 （頁面存檔備份，存於互聯網檔案館）–482. Internet Archive Eprint.
• Peirce, C. S. (1883), "A Theory of probable inference", Studies in Logic, pp. 126-181 （頁面存檔備份，存於互聯網檔案館）, Little, Brown, and Company. (Reprinted 1983, John Benjamins Publishing Company, ISBN 90-272-3271-7)
• Pfanzagl, Johann; with the assistance of R. Hamböker. Parametric Statistical Theory. Berlin: Walter de Gruyter. 1994. ISBN 3-11-013863-8. MR 1291393. 
• Rissanen, Jorma. Stochastic Complexity in Statistical Inquiry. Series in Computer Science 15. Singapore: World Scientific. 1989. ISBN 9971-5-0859-1. MR 1082556. 
• Soofi, Ehsan S. Principal information-theoretic approaches (Vignettes for the Year 2000: Theory and Methods, ed. by George Casella). Journal of the American Statistical Association. December 2000, 95 (452): 1349–1353. JSTOR 2669786. MR 1825292. doi:10.1080/01621459.2000.10474346. 
• Traub, Joseph F.; Wasilkowski, G. W.; Wozniakowski, H. Information-Based Complexity. Academic Press. 1988. ISBN 0-12-697545-0. 
• Zabell, S. L. R. A. Fisher and Fiducial Argument. Statistical Science. Aug 1992, 7 (3): 369–387. JSTOR 2246073. doi:10.1214/ss/1177011233. 

延伸閱讀

• Casella, G., Berger, R.L. (2001). Statistical Inference. Duxbury Press. ISBN 0-534-24312-6
• Freedman, D.A. Statistical models and shoe leather. Sociological Methodology. 1991, 21: 291–313. JSTOR 270939. doi:10.2307/270939. 
• Held L., Bové D.S. (2014). Applied Statistical Inference—Likelihood and Bayes (Springer).
• Lenhard, Johannes. Models and Statistical Inference: the controversy between Fisher and Neyman–Pearson (PDF). British Journal for the Philosophy of Science. 2006, 57: 69–91 [2018-12-29]. doi:10.1093/bjps/axi152. （原始內容存檔 (PDF)於2021-03-03）. 
• Lindley, D. Fiducial distribution and Bayes' theorem. Journal of the Royal Statistical Society, Series B. 1958, 20: 102–7. 
• Rahlf, Thomas (2014). "Statistical Inference", in Claude Diebolt, and Michael Haupert (eds.), "Handbook of Cliometrics ( Springer Reference Series)", Berlin/Heidelberg: Springer. http://www.springerreference.com/docs/html/chapterdbid/372458.html （頁面存檔備份，存於互聯網檔案館）
• Reid, N.; Cox, D. R. On Some Principles of Statistical Inference. International Statistical Review. 2014, 83 (2): n/a. doi:10.1111/insr.12067. 
• Young, G.A., Smith, R.L. (2005). Essentials of Statistical Inference, CUP. ISBN 0-521-83971-8

相關條目

• 統計學
• 獨立性檢驗

外部連結

• MIT OpenCourseWare （頁面存檔備份，存於互聯網檔案館）: Statistical Inference
• NPTEL Statistical Inference （頁面存檔備份，存於互聯網檔案館）, youtube link （頁面存檔備份，存於互聯網檔案館）
• Statistical induction and prediction