Search results
Results from the WOW.Com Content Network
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data.This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable.
The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the E step. These parameter-estimates are then ...
When the first step is a maximum likelihood estimator, under some assumptions, two-step M-estimator is more asymptotically efficient (i.e. has smaller asymptotic variance) than M-estimator with known first-step parameter. Consistency and asymptotic normality of the estimator follows from the general result on two-step M-estimators. [4] Let {V i ...
For example, a maximum-likelihood estimate is the point where the derivative of the likelihood function with respect to the parameter is zero; thus, a maximum-likelihood estimator is a critical point of the score function. [8] In many applications, such M-estimators can be thought of as estimating characteristics of the population.
The EM algorithm consists of two steps: the E-step and the M-step. Firstly, the model parameters and the () can be randomly initialized. In the E-step, the algorithm tries to guess the value of () based on the parameters, while in the M-step, the algorithm updates the value of the model parameters based on the guess of () of the E-step.
An alternative derivation of the maximum likelihood estimator can be performed via matrix calculus formulae (see also differential of a determinant and differential of the inverse matrix). It also verifies the aforementioned fact about the maximum likelihood estimate of the mean. Re-write the likelihood in the log form using the trace trick:
Scoring algorithm, also known as Fisher's scoring, [1] is a form of Newton's method used in statistics to solve maximum likelihood equations numerically, named after Ronald Fisher. Sketch of derivation
When the parameters are estimated using the log-likelihood for the maximum likelihood estimation, each data point is used by being added to the total log-likelihood. As the data can be viewed as an evidence that support the estimated parameters, this process can be interpreted as "support from independent evidence adds", and the log-likelihood ...