Likelihood function
Likelihood function is a fundamental concept in statistical inference, particularly in maximum likelihood estimation. It is a function of the parameters of a statistical model, given specific observed data. The likelihood of a set of parameter values, given outcomes x, is equal to the probability of those observed outcomes given those parameter values.
Definition[edit | edit source]
In the context of a statistical model, a likelihood function (often simply the likelihood) measures the goodness of fit of a statistical model to a sample of data for given values of the unknown parameters. It is formed from the joint probability distribution of the sample, but viewed and used as a function of the parameters only, thus treating the random variables as fixed at the observed values.
Properties[edit | edit source]
The likelihood function has several important properties that can be used in the process of parameter estimation. These include invariance to one-to-one transformations and factorization properties.
Applications[edit | edit source]
The likelihood function is used in a variety of statistical techniques including maximum likelihood estimation, likelihood-ratio test, and Bayesian inference.
See also[edit | edit source]
- Probability density function
- Probability mass function
- Sufficiency (statistics)
- Neyman–Pearson lemma
References[edit | edit source]
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