安德森鸢尾花卉数据集 中变色鸢尾 花萼片宽度数据的分布直方图 推論統計學 ，或称统计推断 （英語：Statistical inference ），指统计学 中，研究如何根据样本 数据去推断总体数量特征的方法。它是在对样本 数据进行描述的基础上，对统计总体的未知数量特征做出以概率 形式表述的推断。更概括地说，是在一段有限的时间内，通过对一个随机过程的观察来进行推断的。
统计学中，统计推断与描述统计 相对应。
统计推断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。
Bandyopadhyay, P. S.; Forster, M. R. (编), 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-XMR 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 BJerzy Neyman and 沃德·亚伯拉罕 )Freedman, D. A. Statistical Models: Theory and practice revised. Cambridge University Press . 2009: xiv+442 pp. ISBN 978-0-521-74385-3MR 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] . （原始内容存档 (PDF) 于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 原始内容 存档于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 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 Peirce, C. S. (1877–1878), "Illustrations of the logic of science" (series), Popular Science Monthly (1878 March), "The Doctrine of Chances", Popular Science Monthly , v. 12, March issue, pp. 604 （页面存档备份 ，存于互联网档案馆 ）–615. Internet Archive Eprint .
(1878 March), "The Doctrine of Chances", Popular Science Monthly , v. 12, March issue, pp. 604 （页面存档备份 ，存于互联网档案馆 ）–615. Internet Archive Eprint .
(1878 June), "The Order of Nature", Popular Science Monthly , v. 13, pp. 203 （页面存档备份 ，存于互联网档案馆 ）–217.Internet Archive Eprint .
(1878 August), "Deduction, Induction, and Hypothesis", Popular Science Monthly , v. 13, pp. 470 （页面存档备份 ，存于互联网档案馆 ）–482. Internet Archive Eprint . Peirce, C. S. (1883), "A Theory of probable inference", Studies in Logic , pp. 126-181 （页面存档备份 ，存于互联网档案馆 ）, 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 3-11-013863-8MR 1291393 Rissanen, Jorma . Stochastic Complexity in Statistical Inquiry. Series in Computer Science 15 . Singapore: World Scientific . 1989. ISBN 9971-5-0859-1MR 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
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 存档 (PDF) 于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 （页面存档备份 ，存于互联网档案馆 ）
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
