Likelihood Ratio

The likelihood ratio is used to compare different data models, perform hypothesis tests, and construct confi-dence intervals. The likelihood of a model is a measure of how well the model fits the observed data. Model likelihood is most often used when fitting a parametric model (e.g., a normal distribution) to data to find the parameters that best describe the data. The general formula for the likelihood function is

where

θ is the model parameterization,

D is the observed data,

L(θ|D) is the likelihood of the model parameterization given the observed data D, and

P(D|θ) is the probability density function of the data given the model parameterization θ.

The basis for this formulation of the likelihood function is best understood by using Bayes's theorem to calculate the probability of the model given ...