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  2. Maximum likelihood estimation - Wikipedia

    en.wikipedia.org/wiki/Maximum_likelihood_estimation

    Using maximum likelihood estimation, the coin that has the largest likelihood can be found, given the data that were observed. By using the probability mass function of the binomial distribution with sample size equal to 80, number successes equal to 49 but for different values of p (the "probability of success"), the likelihood function ...

  3. Expectation–maximization algorithm - Wikipedia

    en.wikipedia.org/wiki/Expectation–maximization...

    Finding a maximum likelihood solution typically requires taking the derivatives of the likelihood function with respect to all the unknown values, the parameters and the latent variables, and simultaneously solving the resulting equations. In statistical models with latent variables, this is usually impossible.

  4. Likelihood function - Wikipedia

    en.wikipedia.org/wiki/Likelihood_function

    For maximum likelihood estimation, the existence of a global maximum of the likelihood function is of the utmost importance. By the extreme value theorem, it suffices that the likelihood function is continuous on a compact parameter space for the maximum likelihood estimator to exist. [7]

  5. Estimation of covariance matrices - Wikipedia

    en.wikipedia.org/wiki/Estimation_of_covariance...

    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:

  6. Binomial regression - Wikipedia

    en.wikipedia.org/wiki/Binomial_regression

    The likelihood function is more fully specified by defining the formal parameters μ i as parameterised functions of the explanatory variables: this defines the likelihood in terms of a much reduced number of parameters. Fitting of the model is usually achieved by employing the method of maximum likelihood to determine these parameters. In ...

  7. Empirical Bayes method - Wikipedia

    en.wikipedia.org/wiki/Empirical_Bayes_method

    To apply empirical Bayes, we will approximate the marginal using the maximum likelihood estimate (MLE). But since the posterior is a gamma distribution, the MLE of the marginal turns out to be just the mean of the posterior, which is the point estimate E ⁡ ( θ ∣ y ) {\displaystyle \operatorname {E} (\theta \mid y)} we need.

  8. Baum–Welch algorithm - Wikipedia

    en.wikipedia.org/wiki/Baum–Welch_algorithm

    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 be a discrete hidden random variable with possible values (i.e. We assume there are states in total).

  9. Fisher information - Wikipedia

    en.wikipedia.org/wiki/Fisher_information

    The role of the Fisher information in the asymptotic theory of maximum-likelihood estimation was emphasized and explored by the statistician Sir Ronald Fisher (following some initial results by Francis Ysidro Edgeworth). The Fisher information matrix is used to calculate the covariance matrices associated with maximum-likelihood estimates.