Editing Likelihood function (section)

====Bayesian interpretation====
In [[Bayesian inference]], although one can speak about the likelihood of any proposition or [[random variable]] given another random variable: for example the likelihood of a parameter value or of a [[statistical model]] (see [[marginal likelihood]]), given specified data or other evidence,<ref name='good1950'>I. J. Good: ''Probability and the Weighing of Evidence'' (Griffin 1950), §6.1</ref><ref name='jeffreys1983'>H. Jeffreys: ''Theory of Probability'' (3rd ed., Oxford University Press 1983), §1.22</ref><ref name='jaynes2003'>E. T. Jaynes: ''Probability Theory: The Logic of Science'' (Cambridge University Press 2003),  §4.1</ref><ref name='lindley1980'>D. V. Lindley: ''Introduction to Probability and Statistics from a Bayesian Viewpoint. Part 1: Probability'' (Cambridge University Press 1980), §1.6</ref> the likelihood function remains the same entity, with the additional interpretations of (i) a [[Conditional probability distribution|conditional density]] of the data given the parameter (since the parameter is then a random variable) and (ii) a measure or amount of information brought by the data about the parameter value or even the model.<ref name='good1950'/><ref name='jeffreys1983'/><ref name='jaynes2003'/><ref name='lindley1980'/><ref name='gelmanetal2014'>A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, D. B. Rubin: ''Bayesian Data Analysis'' (3rd ed., Chapman & Hall/CRC 2014), §1.3</ref> Due to the introduction of a probability structure on the parameter space or on the collection of models, it is possible that a parameter value or a statistical model have a large likelihood value for given data, and yet have a low ''probability'', or vice versa.<ref name='jaynes2003'/><ref name='gelmanetal2014'/> This is often the case in medical contexts.<ref>{{citation |first1=H. C. |last1=Sox |first2=M. C. |last2=Higgins |first3=D. K. |last3=Owens |title=Medical Decision Making |edition=2nd |publisher=Wiley |year=2013 |doi=10.1002/9781118341544 |isbn=9781118341544 |at=chapters 3–4 }}</ref> Following [[Bayes' Rule]], the likelihood when seen as a conditional density can be multiplied by the [[prior probability]] density of the parameter and then normalized, to give a [[posterior probability]] density.<ref name='good1950'/><ref name='jeffreys1983'/><ref name='jaynes2003'/><ref name='lindley1980'/><ref name="gelmanetal2014"/> More generally, the likelihood of an unknown quantity <math display="inline">X</math> given another unknown quantity <math display="inline">Y</math> is proportional to the ''probability of <math display="inline">Y</math> given <math display="inline">X</math>''.<ref name='good1950'/><ref name='jeffreys1983'/><ref name='jaynes2003'/><ref name='lindley1980'/><ref name='gelmanetal2014'/>