Precision (statistics) in the context of "Likelihood"

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⭐ Core Definition: Precision (statistics)

In statistics, the precision matrix or concentration matrix is the matrix inverse of the covariance matrix or dispersion matrix, .For univariate distributions, the precision matrix degenerates into a scalar precision, defined as the reciprocal of the variance, .

Other summary statistics of statistical dispersion also called precision (or imprecision)include the reciprocal of the standard deviation, ; the standard deviation itself and the relative standard deviation;as well as the standard error and the confidence interval (or its half-width, the margin of error).

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👉 Precision (statistics) in the context of Likelihood

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.

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