In statistics, a likelihood function is a function of the parameters of a statistical model evaluated for a fixed sample of observations, defined as follows: the likelihood of a set of parameter values given some observed outcomes is equal to
Likelihood — The likelihood that any parameter (or set of parameters) should have any assigned value (or set of values) is proportional to the probability that if this were so, the totality of observations should be that observed.
Fisher, Ronald A. "On the probabilitymathematical foundations of those observed outcomes given those parameter valuestheoretical statistics. Likelihood" Philosophical transactions of the Royal Society of London. Series A, containing papers of a mathematical or physical character 222.594-604 (1922): 309-368.
Likelihood functions play a key role in statistical inference, especially methods of estimating a parameter using a statistic (a function of the data).
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