The Azimuth Project
Maximum likelihood estimator

Maximum likelihood estimator


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


Given a model with parameters θ\theta – including a model of the kinds of deviations due to noise – along with a set of data {x i}\{x_i\} believed to be generated from the model, the likelihood L(θ;{x i})L(\theta;\{x_i\}) is the probability of model generating the data. The MLE estimate θ^\hat{\theta} of θ\theta is then

θ^=argmax θL(θ;{x i})\hat{\theta}=\argmax_\theta L(\theta;\{x_i\})

For some models LL has a sufficiently nice form that it can be analytically differentiated and set to zero to determine θ^\hat{\theta}. For more difficult models other techniques are required.