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The log-likelihood function being plotted is used in the computation of the score (the gradient of the log-likelihood) and Fisher information (the curvature of the log-likelihood). Thus, the graph has a direct interpretation in the context of maximum likelihood estimation and likelihood-ratio tests .
In statistics, the likelihood-ratio test is a hypothesis test that involves comparing the goodness of fit of two competing statistical models, typically one found by maximization over the entire parameter space and another found after imposing some constraint, based on the ratio of their likelihoods.
If the likelihood ratio for a test in a population is not clearly better than one, the test will not provide good evidence: the post-test probability will not be meaningfully different from the pretest probability. Knowing or estimating the likelihood ratio for a test in a population allows a clinician to better interpret the result. [7]
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data.This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable.
In statistics, the likelihood principle is the proposition that, given a statistical model, all the evidence in a sample relevant to model parameters is contained in the likelihood function. A likelihood function arises from a probability density function considered as a function
The posterior probability distribution of one random variable given the value of another can be calculated with Bayes' theorem by multiplying the prior probability distribution by the likelihood function, and then dividing by the normalizing constant, as follows:
In statistics, deviance is a goodness-of-fit statistic for a statistical model; it is often used for statistical hypothesis testing.It is a generalization of the idea of using the sum of squares of residuals (SSR) in ordinary least squares to cases where model-fitting is achieved by maximum likelihood.
A likelihood region is the set of all values of θ whose relative likelihood is greater than or equal to a given threshold. In terms of percentages, a p % likelihood region for θ is defined to be. [1] [3] [6]