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Summary|8 Annotations
the likelihood is a function
that associates to each parameter the probability (or probability density) of
observing the given sample
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a sample
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e
,
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realization of a random
vector
,
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distribution of
belongs to a parametric family: there is a set
of real vectors (called the parameter
space) whose elements (called parameters) are put into correspondence with
the distributions that could have generated
;
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a
function of
for fixed
(i.e., for the sample
we have observed), it is called likelihood (or likelihood function) and it is
denoted by
.
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log-likelihood function is the function
defined
by
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by finding the parameter
that maximizes the log-likelihood of the observed sample
.
This is the same as maximizing the likelihood function