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，或稱統計推斷（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，統計推斷與描述統計相對應。
統計推斷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**
 Citation |editor1-first=  P. S. |editor1-last = Bandyopadhyay |editor2-first= M. R. |editor2-last = Forster | title= Philosophy of Statistics |year= 2011 |publisher = Elsevier .- cite book |last1=Bickel |first1=Peter J. |last2 = Doksum |first2 = Kjell A. |title = Mathematical statistics: Basic and selected topics |volume = 1 |edition = Second (updated printing 2007) |year = 2001 |publisher = Prentice Hall |mr = 443141 |isbn = 0-13-850363-X - Cox, D. R. (2006). Principles of Statistical Inference, Cambridge University Press. 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. (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.- dead-url=no - cite journal |doi=10.1198/016214501753168398 |title=Model Selection and the Principle of Minimum Description Length: Review paper |first1=Mark H. |last1=Hansen |first2=Bin |last2=Yu |author2-link=Bin Yu |journal=Journal of the American Statistical Association |volume=96 |issue=454 |date=June 2001 |pages=746–774 |jstor=2670311 |mr=1939352 |url=http://www.stat.berkeley.edu/webmastr/users/binyu/ps/mdl.ps |archive-url=https://web.archive.org/web/20041116080440/http://www.stat.berkeley.edu/webmastr/users/binyu/ps/mdl.ps |dead-url=yes |archive-date=2004-11-16 - cite journal |authorlink=Andrei N. Kolmogorov|first=Andrei N.|last=Kolmogorov |year=1963 |title = On tables of random numbers |journal=Sankhyā Ser. A.|volume=25 |pages=369–375 |mr=178484   Reprinted as  cite journal |first=Andrei N. |last=Kolmogorov |year=1998 |title=On tables of random numbers |journal = Theoretical Computer Science |volume=207 |issue=2 |pages = 387–395 |doi = 10.1016/S0304-3975(98)00075-9 |mr = 1643414 - Konishi S., Kitagawa G. (2008),  Information Criteria and Statistical Modeling, Springer.- Le Cam, Lucian. (1986) Asymptotic Methods of Statistical Decision Theory, Springer. 0-387-96307-3- Moore, D. S.; McCabe, G. P.; Craig, B. A. (2015), Introduction to the Practice of Statistics, Eighth Edition, Macmillan.-  (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 date=20200820040933 –615.  Internet Archive  Eprint.
** (1878 March), "The Doctrine of Chances", Popular Science Monthly, v. 12, March issue, pp.  604 date=20200820040933 –615.  Internet Archive  Eprint.
** (1878 June), "The Order of Nature", Popular Science Monthly, v. 13, pp.  203 date=20200819235024 –217.Internet Archive  Eprint.
** (1878 August), "Deduction, Induction, and Hypothesis", Popular Science Monthly, v. 13, pp.  470 date=20200819235026 –482. Internet Archive  Eprint.
*Peirce, C. S. (1883), "A Theory of probable inference", Studies in Logic, pp.  126-181 date=20190608194831 , Little, Brown, and Company. (Reprinted 1983, John Benjamins Publishing Company, 90-272-3271-7)- cite book |title=Parametric Statistical Theory |last1=Pfanzagl |first1=Johann |authorlink=  
publisher=Walter de Gruyter |location=Berlin |isbn = 3-11-013863-8 |mr = 1291393 - cite book |authorlink=Jorma Rissanen |first=Jorma |last=Rissanen |year=1989 |title = Stochastic Complexity in Statistical Inquiry |location=Singapore |publisher=World Scientific |series = Series in Computer Science |volume=15 |mr=1082556 |isbn = 9971-5-0859-1 - cite journal |title = Principal information-theoretic approaches (Vignettes for the Year 2000: Theory and Methods, ed. by George Casella) |url = https://archive.org/details/sim_journal-of-the-american-statistical-association_2000-12_95_452/page/1349 | last=Soofi |first=Ehsan S.|journal=Journal of the American Statistical Association |volume=95 |issue=452 |date=December 2000 |pages=1349–1353 |jstor=2669786 |mr=1825292 |doi = 10.1080/01621459.2000.10474346 

**延伸閱讀**
Casella, G., Berger, R.L. (2001). Statistical Inference. Duxbury Press. 0-534-24312-6-  jstor = 270939 - Held L., Bové D.S. (2014). Applied Statistical Inference—Likelihood and Bayes (Springer).
*cite journal | last1 = Lenhard | first1 = Johannes | year = 2006 | title = Models and Statistical Inference: the controversy between Fisher and Neyman–Pearson | url = http://www.stats.org.uk/statistical-inference/Lenhard2006.pdf | journal = British Journal for the Philosophy of Science | volume = 57 | issue =  
dead-url = no - cite journal | last1 = Lindley | first1 = D | year = 1958 | title = Fiducial distribution and Bayes' theorem | url = | journal = Journal of the Royal Statistical Society, Series B | volume = 20 | issue = | pages = 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 date=20140714181530 - first2 = D. R. 
*Young, G.A., Smith, R.L. (2005). Essentials of Statistical Inference, CUP. 0-521-83971-8

**相關條目**
 統計學
*獨立性檢驗

**外部連結**
 MIT  OpenCourseWare date=20210224213339 : Statistical Inference-  NPTEL Statistical Inference date=20190611165744 ,  youtube link date=20210308204437 -  Statistical induction and prediction