Index: The Book of Statistical Proofs ▷ General Theorems ▷ Frequentist statistics ▷ Likelihood theory ▷ Maximum likelihood estimation

Definition: Let there be a generative model $m$ describing measured data $y$ using model parameters $\theta$. Then, the parameter values maximizing the likelihood function or log-likelihood function are called “maximum likelihood estimates” of $\theta$:

\[\label{eq:mle} \hat{\theta} = \operatorname*{arg\,max}_\theta \mathcal{L}_m(\theta) = \operatorname*{arg\,max}_\theta \mathrm{LL}_m(\theta) \; .\]

The process of calculating $\hat{\theta}$ is called “maximum likelihood estimation” and the functional form leading from $y$ to $\hat{\theta}$ given $m$ is called “maximum likelihood estimator”. Maximum likelihood estimation, estimator and estimates may all be abbreviated as “MLE”.

 
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Metadata: ID: D60 | shortcut: mle | author: JoramSoch | date: 2020-05-15, 23:05.