Maximum likelihood estimator (Rev #3, changes)

Showing changes from revision #2 to #3:
Added | ~~Removed~~ | ~~Chan~~ged

The **maximum likelihood estimator (MLE)** is one preferred method for esimating the parameters of a partially probabilistic model.

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.

- Maximum likelihood, Wikipedia.

category: ~~ methodology~~ statistical methods