推论统计学

推论统计学，或称统计推断（英语：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。

统计推断的结果常用来决定下一步的作法，可能是要做更深入的试验或问卷，或是是决定是否要实行某项方案。

参考文献

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-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·亚伯拉罕)
Freedman, D. A. Statistical Models: Theory and practice revised. Cambridge University Press. 2009: xiv+442 pp. ISBN 978-0-521-74385-3. 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. 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 （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 3-11-013863-8. 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.

延伸阅读

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. （原始内容存档 (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