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.
Read more about this topic: Likelihood Principle
Famous quotes containing the words law and/or likelihood:
“From the war of nature, from famine and death, the most exalted object which we are capable of conceiving, namely, the production of the higher animals, directly follows. There is grandeur in this view of life, with its several powers, having been breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.”
—Charles Darwin (1809–1882)
“Sustained unemployment not only denies parents the opportunity to meet the food, clothing, and shelter needs of their children but also denies them the sense of adequacy, belonging, and worth which being able to do so provides. This increases the likelihood of family problems and decreases the chances of many children to be adequately prepared for school.”
—James P. Comer (20th century)