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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 ...
The Viterbi algorithm is a dynamic programming algorithm for obtaining the maximum a posteriori probability estimate of the most likely sequence of hidden states—called the Viterbi path—that results in a sequence of observed events.
It is closely related to the method of maximum likelihood (ML) estimation, but employs an augmented optimization objective which incorporates a prior density over the quantity one wants to estimate. MAP estimation is therefore a regularization of maximum likelihood estimation, so is not a well-defined statistic of the Bayesian posterior ...
The Baum–Welch algorithm uses the well known EM algorithm to find the maximum likelihood estimate of the parameters of a hidden Markov model given a set of observed feature vectors. Let X t {\displaystyle X_{t}} be a discrete hidden random variable with N {\displaystyle N} possible values (i.e.
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]
where p(r | x) denotes the conditional joint probability density function of the observed series {r(t)} given that the underlying series has the values {x(t)}. In contrast, the related method of maximum a posteriori estimation is formally the application of the maximum a posteriori (MAP) estimation approach.
Maximum Likelihood (also likelihood) optimality criterion is the process of finding the tree topology along with its branch lengths that provides the highest probability observing the sequence data, while parsimony optimality criterion is the fewest number of state-evolutionary changes required for a phylogenetic tree to explain the sequence data.