maximum-likelihood

For parameters $\theta$, and data $D$, the goal of maximum likelihood estimation is to evaluate:

$\theta_\mathrm{MLE} = \mathrm{arg} \mathrm{max} p(D \vert \theta)$

where $\theta_\mathrm{MLE}$ is also written as $\hat{\theta}$, where the "hat" refers to an estimation.

This is distinct from [[bayesian-parameter-estimation]], where the objective is to learn $p(\theta \vert D)$.