Likelihood Notes
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Likelihood is the hypothetical probability that an event that has already occurred would yield a specific outcome. The concept differs from that of a probability in that a probability refers to the occurrence of future events, while a likelihood refers to past events with known outcomes. A likelihood function is the probability or probability density for the occurrence of a sample configuration , ..., given that the probability density with parameter is known, A quantity used to test nested hypotheses. Let be a nested hypothesis with degrees of freedom within (which has degrees of freedom), then calculate the maximum likelihood of a given outcome, first given , then given . Then Comparison of to the critical value of the chi-squared distribution with degrees of freedom then gives the significance of the increase in likelihood. The term likelihood ratio is also used (especially in medicine) to test nonnested complementary hypotheses as follows, Maximum likelihood, also called the maximum likelihood method, is the procedure of finding the value of one or more parameters for a given statistic which makes the known likelihood distribution a maximum . The maximum likelihood estimate for a parameter is denoted . A maximum likelihood estimator is a value of the parameter such that the likelihood function is a maximum
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Transcript of Likelihood Notes
Likelihood is the hypotheticalprobabilitythat an event that has already occurred would yield a specific outcome. The concept differs from that of a probability in that a probability refers to the occurrence of future events, while a likelihood refers to past events with known outcomes.A likelihood functionis the probability or probability density for the occurrence of a sample configuration, ...,given that the probability densitywith parameteris known,
A quantity used to testnested hypotheses. Letbe anested hypothesiswithdegrees of freedomwithin(which hasdegrees of freedom), then calculate themaximum likelihoodof a given outcome, first given, then given. Then
Comparison ofto the critical value of thechi-squared distributionwithdegrees of freedomthen gives thesignificanceof the increase inlikelihood.The term likelihood ratio is also used (especially in medicine) to test nonnested complementary hypotheses as follows,
Maximum likelihood, also called the maximum likelihood method, is the procedure of finding the value of one or more parameters for a given statistic which makes theknownlikelihooddistribution amaximum. The maximum likelihood estimate for a parameteris denoted.A maximum likelihood estimator is a value of the parametersuch that thelikelihood functionis a maximum
