Editing Likelihood function (section)

===Historical remarks===
{{see also|History of statistics|History of probability}}

The term "likelihood" has been in use in English since at least late [[Middle English]].<ref>"likelihood", ''[[Shorter Oxford English Dictionary]]'' (2007).</ref> Its formal use to refer to a specific [[Function (mathematics)|function]] in mathematical statistics was proposed by [[Ronald Fisher]],<ref>{{Citation | title=On the history of maximum likelihood in relation to inverse probability and least squares| first= A. | last=Hald |author-link=Anders Hald |journal=[[Statistical Science]] |volume= 14| issue=2 |year=1999 | pages =214&ndash;222 | doi=10.1214/ss/1009212248 | jstor = 2676741|url=http://projecteuclid.org/download/pdf_1/euclid.ss/1009212248 |mode=cs1 | doi-access=free }}</ref> in two research papers published in 1921<ref>{{citation
 | last=Fisher | first=R.A. |author-link=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 |mode=cs1 }}</ref> and 1922.<ref name=Fisher1922>{{citation
 | last=Fisher | first=R.A. |author-link=Ronald Fisher
 | journal= Philosophical Transactions of the Royal Society A
 | title=On the mathematical foundations of theoretical statistics
 | volume=222 | issue=594–604 | year=1922 | pages=309–368
 | url=http://digital.library.adelaide.edu.au/dspace/handle/2440/15172
 | jstor=91208 | jfm = 48.1280.02 |doi=10.1098/rsta.1922.0009
| bibcode=1922RSPTA.222..309F |mode=cs1 | doi-access=free | hdl=2440/15172 | hdl-access=free }}</ref> The 1921 paper introduced what is today called a "likelihood interval"; the 1922 paper introduced the term "[[method of maximum likelihood]]". Quoting Fisher:

{{Cquote|[I]n 1922, I proposed the term 'likelihood,' in view of the fact that, with respect to [the parameter], it is not a probability, and does not obey the laws of probability, while at the same time it bears to the problem of rational choice among the possible values of [the parameter] a relation similar to that which probability bears to the problem of predicting events in games of chance. . . . Whereas, however, in relation to psychological judgment, likelihood has some resemblance to probability, the two concepts are wholly distinct. . . ."<ref>{{citation |last=Klemens |first=Ben |title=Modeling with Data: Tools and Techniques for Scientific Computing |publisher= [[Princeton University Press]] |year=2008 |page=329 |mode=cs1 }}</ref>}}

The concept of likelihood should not be confused with probability as mentioned by Sir Ronald Fisher

{{Cquote|I stress this because in spite of the emphasis that I have always laid upon the difference between probability and likelihood there is still a tendency to treat likelihood as though it were a sort of probability. The first result is thus that there are two different measures of rational belief appropriate to different cases. Knowing the population we can express our incomplete knowledge of, or expectation of, the sample in terms of probability; knowing the sample we can express our incomplete knowledge of the population in terms of likelihood.<ref>{{citation
  | last = Fisher | first = Ronald | authorlink=Ronald Fisher
  | title = Inverse Probability
  | year = 1930
  | journal = [[Mathematical Proceedings of the Cambridge Philosophical Society]]
  | volume = 26 | issue = 4
  | pages= 528–535
  | doi = 10.1017/S0305004100016297
  | bibcode = 1930PCPS...26..528F
 |mode=cs1 }}</ref>}}

Fisher's invention of statistical likelihood was in reaction against an earlier form of reasoning called [[inverse probability]].<ref>{{citation | last1 = Fienberg | first1 = Stephen E | year = 1997 | title = Introduction to R.A. Fisher on inverse probability and likelihood | journal = [[Statistical Science]] | volume = 12 | issue = 3| page = 161 | doi = 10.1214/ss/1030037905 |mode=cs1 | doi-access = free }}</ref> His use of the term "likelihood" fixed the meaning of the term within mathematical statistics.

[[A. W. F. Edwards]] (1972) established the axiomatic basis for use of the log-likelihood ratio as a measure of relative support for one hypothesis against another. The ''support function'' is then the natural logarithm of the likelihood function. Both terms are used in [[phylogenetics]], but were not adopted in a general treatment of the topic of statistical evidence.<ref>{{citation |last=Royall |first=R. |year=1997 |title=Statistical Evidence |publisher=[[Chapman & Hall]] |mode=cs1 }}</ref>