This website is using cookies to ensure you get the best experience possible on our website.
More info: Privacy & Cookies, Imprint
The maximum likelihood (ML) method is a statistical technique for estimating the parameters of a probability distribution based on observed data. It is used in various areas of statistics and machine learning.
The basic idea of the ML method is to choose the parameters of a distribution in such a way that the observed data is the most likely. The probability is expressed by the likelihood function. The likelihood function indicates how probable the observed data is given certain parameter values.
The estimation process of the ML method consists of the following steps:
Assume a Probability Distribution: First, a probability distribution is chosen that represents the model for the data. For example, one might assume that the data follows a normal distribution.
Construction of the likelihood function: Based on the assumption of the distribution model, the likelihood function is constructed. This function gives the probability of the observed data depending on the parameters of the distribution.
Maximization of the likelihood function: The parameter values are chosen in such a way that the likelihood function is maximized. This can be achieved using optimization methods such as the Newton-Raphson method or the gradient descent method.
Estimation of the parameters: After the likelihood function has been maximized, one obtains the estimated parameter values that best explain the observed data.
The ML method has many applications, including estimating parameters in linear regressions, logistic regressions, Gaussian mixtures, and many other statistical models. It is also used in machine vision, speech recognition, text analysis, and other machine learning areas to fit models to data and make predictions.
It is important to note that the ML method is based on certain assumptions and is not always the best estimation method for all situations. In some cases, other estimation methods such as Bayesian estimation or robust estimation methods may be more advantageous.