Point estimation in the context of Parameter

A likelihood function (often simply called the likelihood) measures how well a statistical model explains observed data by calculating the probability of seeing that data under different parameter values of the model. It is constructed from the joint probability distribution of the random variable that (presumably) generated the observations. When evaluated on the actual data points, it becomes a function solely of the model parameters.

In maximum likelihood estimation, the model parameter(s) or argument that maximizes the likelihood function serves as a point estimate for the unknown parameter, while the Fisher information (often approximated by the likelihood's Hessian matrix at the maximum) gives an indication of the estimate's precision.

In statistics, interval estimation is the use of sample data to estimate an interval of possible values of a (sample) parameter of interest. This is in contrast to point estimation, which gives a single value.

The most prevalent forms of interval estimation are confidence intervals (a frequentist method) and credible intervals (a Bayesian method). Less common forms include likelihood intervals, fiducial intervals, tolerance intervals, and prediction intervals. For a non-statistical method, interval estimates can be deduced from fuzzy logic.