data
points
is given. A likelihood function
gives the probability that the observed data would
result from the proposed stochastic mechanism relative to all other possible
outcomes [132]. The data
is a realization of the random variable
.
On the log scale,
is a realization of the random variable
The likelihood function
is
where
is the joint probability distribution function (pdf) that
occurs given that
oc-curs. This is a normal pdf with mean
and variance
.
Thus,
and
The maximum likelihood parameter estimates are those values of the parameters
that maximize
,
or equivalently that maximize
.
A calculation
shows
where
are the log-residuals. The critical points
of
are zeroes of the
derivatives
i.e., are roots of the uncoupled equations
