Maximum Likelihood Estimation
/ˈmæksɪməm ˈlaɪklihʊd ˌɛstɪˈmeɪʃən/max·i·mum like·li·hood es·ti·ma·tionnoun
Definition
1.[in statistics] a method that picks the parameter values under which the observed data would have been most probable, by maximising the probability the model assigns to that data.
Maximum likelihood estimation gives the sample mean as the estimator for a Gaussian's centre.
Formal statement
theta_hat = argmax_theta sum_i log p(x_i | theta)The log turns a product into a sum without moving the maximum.
Etymology
From Latin maximus 'greatest' and aestimare 'to value', with likelihood, Middle English liklihede, in the technical sense Ronald Fisher gave it in 1922 to distinguish it from probability: a function of the parameter given fixed data, not of the data.
Antonyms
- maximum a posteriori estimationsense 1 · Relational
See also
References
- Fisher, R. A. (1922). On the Mathematical Foundations of Theoretical Statistics.Philosophical Transactions of the Royal Society A, 222, 309–368.