推論統計學
統計學名詞
(重定向自统计推断)
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。
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.
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- 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
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- 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
相关条目
外部連結
- MIT OpenCourseWare (页面存档备份,存于互联网档案馆): Statistical Inference
- NPTEL Statistical Inference (页面存档备份,存于互联网档案馆), youtube link (页面存档备份,存于互联网档案馆)
- Statistical induction and prediction