Maximum likelihood estimation is a principle of statistical parameter estimation in which the parameter vector theta of an assumed generative model is chosen to maximise the likelihood function L(theta) = P(X | theta), where the observed data X is held fixed and theta varies — hence it is a function of the parameters, not of the data, despite being written as a probability of the data. Under Bayes' rule the posterior P(theta | X) is proportional to P(X | theta) times the prior, so with a uniform (uninformative) prior maximising the posterior reduces exactly to maximising the likelihood. Assuming independent and identically distributed samples factorises the likelihood into a product of per-observation probabilities, which is conventionally converted to a log-likelihood sum and maximised by setting its derivative to zero; this framework underlies discriminative model fitting such as logistic regression and provides the plug-in route to predicting new observations.
Maximum likelihood estimation is a principle of statistical parameter estimation in which the parameter vector theta of an assumed generative model is chosen to maximise the likelihood function L(the…