| 释义 |
- Relation with other theories
- Criticism
- History
- See also
- References
- Further reading
- External links
Likelihoodist statistics or likelihoodism is an approach to statistics that exclusively or primarily uses the likelihood function. Likelihoodist statistics is a more minor school than the main approaches of Bayesian statistics and frequentist statistics, but has some adherents and applications. The central idea of likelihoodism is the likelihood principle: data are interpreted as evidence, and the strength of the evidence is measured by the likelihood function. Beyond this, there are significant differences within likelihood approaches: "orthodox" likelihoodists consider data only as evidence, and do not use it as the basis of statistical inference, while others make inferences based on likelihood, but without using Bayesian inference or frequentist inference. Likelihoodism is thus criticized for either not providing a basis for belief or action (if it fails to make inferences), or not satisfying the requirements of these other schools. The likelihood function is also used in Bayesian statistics and frequentist statistics, but they differ in how it is used. Some likelihoodists consider their use of likelihood as an alternative to other approaches, while others consider it complementary and compatible with other approaches; see {{slink||Relation with other theories}}. Relation with other theories {{section-empty|date=March 2019}} Criticism {{section-empty|date=March 2019}} History Likelihoodism as a distinct school dates to {{harvtxt|Edwards|1972}}, which gives a systematic treatment of statistics, based on likelihood. This built on significant earlier work; see {{harvtxt|Dempster|1972}} for a contemporary review. While comparing ratios of probabilities dates to early statistics and probability, notably Bayesian inference as developed by Pierre-Simon Laplace from the late 1700s, likelihood as a distinct concept is due to Ronald Fisher in {{harvtxt|Fisher|1921}}. Likelihood played an important role in Fisher's statistics, but he developed and used many non-likelihood frequentist techniques as well. His late writings, notably {{harvtxt|Fisher|1955}}, emphasize likelihood more strongly, and can be considered an precursor to a systematic theory of likelihoodism. The likelihood principle was proposed in 1962 by several authors, notably {{harvtxt|Barnard|Jenkins|Winsten|1962}}, {{harvtxt|Birnbaum|1962}}, and {{harvtxt|Savage|1962}}, and followed by the law of likelihood in {{harvtxt|Hacking|1965}}; these laid the foundation for likelihoodism. See {{slink|Likelihood principle|History}} for early history. While Edwards's version of likelihoodism considered likelihood as only evidence, which was followed by {{harvtxt|Royall|1997}}, others proposed inference based only on likelihood, notably as extensions of maximum likelihood estimation. Notable is John Nelder, who declared in {{Harvtxt|Nelder|1999|p=264}}: {{quote|At least once a year I hear someone at a meeting say that there are two modes of inference: frequentist and Bayesian. That this sort of nonsense should be so regularly propagated shows how much we have to do. To begin with there is a flourishing school of likelihood inference, to which I belong.}}Textbooks that take a likelihoodist approach include the following: {{harvtxt|Kalbfleisch|1986}}, {{harvtxt|Azzalini |1996}}, {{harvtxt|Pawitan|2001}}, {{harvtxt|Rohde|2014}}, and {{harvtxt|Held|Sabanés Bové|2014}}. A collection of relevant papers is given by {{harvtxt|Taper|Lele|2004}}. See also- Akaike information criterion
- Foundations of statistics
- Likelihood ratio test
References {{refbegin}}- {{citation| last= Azzalini | first= Adelchi | title= Statistical Inference—Based on the likelihood | year= 1996 | publisher= Chapman & Hall}}
- {{citation|last=Barnard|first=G. A. |author2-first=G. M. |author2-last=Jenkins |author3-first=C. B. |author3-last=Winsten|author1-link=George Alfred Barnard | author2-link= Gwilym Jenkins|year=1962|title=Likelihood inference and time series|jstor=2982406|journal=Journal of the Royal Statistical Society, Series A|volume=125|issue=3|pages=321–372|doi=10.2307/2982406}}
- {{citation|last=Birnbaum|first=Allan|authorlink=Allan Birnbaum|year=1962|title=On the foundations of statistical inference |jstor=2281640|journal=Journal of the American Statistical Association |volume=57|issue=298|pages=269–326|doi= 10.2307/2281640|mr=0138176}} (With discussion.)
- {{citation|title=[Book Review] Likelihood. An Account of the Statistical Concept of Likelihood and Its Application to Scientific Inference. A. W. F. Edwards. Cambridge University Press, New York, 1972. xvi, 236 pp., illus. $13.50 |first=A. P. |last=Dempster |journal=Science |year=1972 |volume=177 |number=4052 |pages=878-879 |doi=10.1126/science.177.4052.878}}
- {{citation|last=Edwards|first=Anthony W. F.|authorlink=A. W. F. Edwards|title=Likelihood|edition=1st|publisher= Cambridge University Press|year=1972|isbn=}}
- {{citation|last=Edwards|first=Anthony W. F.|authorlink=A. W. F. Edwards|title=Likelihood|edition= 2nd|publisher=Johns Hopkins University Press|year=1992|isbn=0-8018-4445-2}}
- {{citation | last=Fisher | first=R. A. |authorlink=Ronald Fisher | journal= Metron| title= On the "probable error" of a coefficient of correlation deduced from a small sample | volume=1 | year=1921 | pages=3–32}}
- {{citation |last=Fisher |first=Ronald |authorlink=Ronald Fisher |year = 1955 | journal = Journal of the Royal Statistical Society, Series B | volume = 17 | pages = 69–78 | title = Statistical methods and scientific induction }}
- {{citation|last=Hacking|first=Ian|authorlink=Ian Hacking|title=Logic of Statistical Inference |publisher= Cambridge University Press|year=1965|isbn=0-521-05165-7}}
- {{citation|first1= Leonhard | last1= Held | first2= Daniel | last2= Sabanés Bové | title= Applied Statistical Inference—Likelihood and Bayes | year= 2014 | publisher= Springer}}
- {{citation | author-last= Kalbfleisch | author-first= J. G. | author-link= James G. Kalbfleisch | year= 1985 | title= Probability and Statistical Inference | volume= 2 | publisher= Springer-Verlag}}
- {{citation|first=John A. |last=Nelder |authorlink=John Nelder |title=From statistics to statistical science |journal=Journal of the Royal Statistical Society. Series D (The Statistician) |volume=48 |number=2 |year=1999 |pages=257-269 |jstor=2681191}}
- {{citation|title=In All Likelihood: Statistical Modelling And Inference Using Likelihood |isbn=978-0-19967122-9 |first=Yudi |last=Pawitan |year=2001 | publisher= Oxford University Press}}
- {{citation|last=Rohde |first=Charles A. |year=2014 |title=Introductory Statistical Inference with the Likelihood Function |publisher= Springer |isbn=978-3-319-10460-7}}
- {{citation|last=Royall|first=Richard M.|title=Statistical Evidence: A Likelihood Paradigm|edition=|publisher=Chapman & Hall|year=1997|isbn=0-412-04411-0}}
- {{citation|last=Savage|first=Leonard J.|authorlink=Leonard J. Savage|title=The Foundations of Statistical Inference|edition=|publisher=Methuen Publishing|year=1962|isbn=|display-authors=etal}}
- {{citation|editor1-last=Taper | editor1-first= M. L. |editor2-last=Lele | editor2-first= S. R. |year=2004 |title=The Nature of Scientific Evidence | publisher= University of Chicago Press}}
{{refend}} Further reading {{refbegin}}- {{citation |first=Greg |last=Gandenberger |title=Why I am not a likelihoodist |year=2016 |volume=16 |number=7 |pages=1-22 |hdl=2027/spo.3521354.0016.007 |journal=Philosophers' Imprint}}
{{refend}} External links - {{cite web |url=https://plato.stanford.edu/entries/logic-inductive/sup-likelihood.html |title=Likelihood Ratios, Likelihoodism, and the Law of Likelihood |work=Stanford Encyclopedia of Philosophy |access-date=2019-03-14}}
1 : Likelihoodist statistics |