Likelihood | Bayesian statistics

Likelihood function

The likelihood function (often simply called the likelihood) is the joint probability of the observed data viewed as a function of the parameters of the chosen statistical model. To emphasize that the likelihood is a function of the parameters, the sample is taken as observed, and the likelihood function is often written as . Equivalently, the likelihood may be written to emphasize that it is the probability of observing sample given , but this notation is less commonly used. According to the likelihood principle, all of the information a given sample provides about is expressed in the likelihood function. In maximum likelihood estimation, the value which maximizes the probability of observing the given sample, i.e. , serves as a point estimate for . Meanwhile in Bayesian statistics, the likelihood function is the conduit through which sample information influences , the posterior probability of the parameter, via Bayes' rule. (Wikipedia).

Likelihood function
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