Описание тега log-likelihood

Given a sample and a parametric family of distributions (i.e., a set of distributions indexed by a parameter) that could have generated the sample, the Likelihood is a function that associates to each parameter the probability (or probability density) of observing the given sample.

The log-Likelihood a function which is the natural logarithm of the Likelihood function

For many applications, the log-Likelihood, is more convenient to work with as compared to the Likelihood. This is because we are generally interested in where the Likelihood reaches its maximum value. Since the logarithm is a strictly increasing function, the logarithm of a function achieves its maximum value at the same points as the function itself, hence the log-likelihood can be used in place of the likelihood for maximum likelihood estimation and related techniques.

Finding the maximum of a function often involves taking the derivative of a function and solving for the parameter being maximized, and this is often easier when the function being maximized is a log-likelihood rather than the original likelihood function, because the probability of the conjunction of several independent variables is the product of probabilities of the variables and solving an additive equation is usually easier than a multiplicative one.