Maximum likelihood estimation is a common approach used for parameter estimation in statistical models. Here are the key aspects of maximum likelihood:
Given a statistical model with parameters and some data, the method estimates the set of parameters that maximize the likelihood or probability of observing the given data.
Likelihood is the conditional probability of obtaining the sample data given the parameters of the distribution.
Maximizing likelihood finds the parameters that make the observed data most probable or likely.
For example, in linear regression the parameters (slope, intercept) that maximize the Gaussian likelihood of the residuals are estimated.
Common methods used for maximization include iterative procedures like gradient ascent.
In statistics, maximum likelihood produces consistent, efficient and asymptotically normal estimates under regularity conditions.
Used widely in building probabilistic models like logistic regression, Naive Bayes, mixture models etc.
Provides natural way to estimate structured probabilistic models with latent variables.
Objectively evaluates which parameter values best “explain” the data without making prior assumptions.
So in summary, maximum likelihood is a principled way to estimate parameters of statistical distributions from observed data in an objective, model-consistent manner.