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Concept
Likelihoodist statistics
Summary
Likelihoodist statistics or likelihoodism is an approach to statistics that exclusively or primarily uses the likelihood function. Likelihoodist statistics is a more minor school than the main approaches of Bayesian statistics and frequentist statistics, but has some adherents and applications. The central idea of likelihoodism is the likelihood principle: data are interpreted as evidence, and the strength of the evidence is measured by the likelihood function. Beyond this, there are significant differences within likelihood approaches: "orthodox" likelihoodists consider data only as evidence, and do not use it as the basis of statistical inference, while others make inferences based on likelihood, but without using Bayesian inference or frequentist inference. Likelihoodism is thus criticized for either not providing a basis for belief or action (if it fails to make inferences), or not satisfying the requirements of these other schools.
The likelihood function is also used in Bayesian statistics and frequentist statistics, but they differ in how it is used. Some likelihoodists consider their use of likelihood as an alternative to other approaches, while others consider it complementary and compatible with other approaches; see .
While likelihoodism is a distinct approach to statistical inference, it can be related to or contrasted with other theories and methodologies in statistics. Here are some notable connections:
Bayesian statistics: Bayesian statistics is an alternative approach to statistical inference that incorporates prior information and updates it using observed data to obtain posterior probabilities. Likelihoodism and Bayesian statistics are compatible in the sense that both methods utilize the likelihood function. However, they differ in their treatment of prior information. Bayesian statistics incorporates prior beliefs into the analysis explicitly, whereas likelihoodism focuses solely on the likelihood function without specifying a prior distribution.
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