High Quality Content by WIKIPEDIA articles! In statistics, the likelihood function is a function of the parameters of a statistical model that plays a key role in statistical inference. In non-technical parlance, "likelihood" is usually a synonym for "probability," but in statistical usage there is a clear distinction in perspective: the number that is the probability of some observed outcomes given a set of parameter values is regarded as the likelihood of the set of parameter values given the observed outcomes. Mathematically, writing X for the set of observed data and ? for the set of parameter values, the expression P(X | ?), the probability of X given ?, can be interpreted as the expression L(? | X), the likelihood of ? given X. The interpretation of L(? | X) as a function of ? is especially obvious when X is fixed and ? is allowed to vary.

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