Likelihood Principle - The Law of Likelihood

The Law of Likelihood

A related concept is the law of likelihood, the notion that the extent to which the evidence supports one parameter value or hypothesis against another is equal to the ratio of their likelihoods. That is,

is the degree to which the observation x supports parameter value or hypothesis a against b. If this ratio is 1, the evidence is indifferent, and if greater or less than 1, the evidence supports a against b or vice versa. The use of Bayes factors can extend this by taking account of the complexity of different hypotheses.

Combining the likelihood principle with the law of likelihood yields the consequence that the parameter value which maximizes the likelihood function is the value which is most strongly supported by the evidence. This is the basis for the widely-used method of maximum likelihood.