Likelihood measures how well a value of a parameter in a statistical model accounts for observed
data. If a statistical model with parameter 
assigns probability
mass or probability density function 
to fixed data 
, its likelihood function
is
 |
Here 
is fixed and 
varies. Thus 
is not generally a probability
over values of the parameter and need not sum or integrate
to 1 as a function of 
(Hoel 1962, Casella and Berger 2002).
Common uses include maximum likelihood estimation, comparison of hypotheses by a likelihood ratio, and combination with a prior distribution in Bayesian analysis. The log-likelihood function is often used in computation because it converts products into sums without changing the maximizing values of the parameter; its derivative is the score function.
In graph theory, graph likelihood is a separate notion: the probability that a specified simple graph is produced by a particular random sequential construction.
