# Maximum likelihood estimator # * toc {: toc} ## Idea ## The **maximum likelihood estimator (MLE)** is one preferred method for esimating the parameters of a partially probabilistic model. ## Details ## Given a model with parameters $\theta$ -- including a model of the kinds of deviations due to noise -- along with a set of data $\{x_i\}$ believed to be generated from the model, the _likelihood_ $L(\theta;\{x_i\})$ is the probability of model generating the data. The MLE estimate $\hat{\theta}$ of $\theta$ is then $$\hat{\theta}=\argmax_\theta L(\theta;\{x_i\})$$ For some models $L$ has a sufficiently nice form that it can be analytically differentiated and set to zero to determine $\hat{\theta}$. For more difficult models other techniques are required. ## References ## * [Maximum likelihood](http://en.wikipedia.org/wiki/Maximum_likelihood_estimation), Wikipedia. category:statistical methods [[!redirects maximum likelihood estimator]] [[!redirects Maximum likelihood estimation]] [[!redirects maximum likelihood estimation]]