The :class:`~symfit.core.objectives.LogLikelihood` objective function should be used to perform log-likelihood maximization. The :meth:`~symfit.core.objectives.LogLikelihood.__call__` and :meth:`~symfit.core.objectives.LogLikelihood.eval_jacobian` definitions have been changed to facilitate what one would expect from Likelihood fitting:
__call__ gives the value of log-likelihood at the given values of \vec{p} and \vec{x}_i, where \vec{p} is a shorthand notation for all parameter, and \vec{x}_i the same shorthand for all independent variables.
\log{L(\vec{p}|\vec{x}_i)} = \sum_{i=1}^{N} \log{f(\vec{p}|\vec{x}_i)}
:meth:`~symfit.core.objectives.LogLikelihood.eval_jacobian` gives the derivative with respect to every parameter of the log-likelihood:
\nabla_{\vec{p}} \log{L(\vec{p}|\vec{x}_i)} = \sum_{i=1}^{N}
\frac{1}{f(\vec{p}|\vec{x}_i)} \nabla_{\vec{p}} f(\vec{p}|\vec{x}_i)
Where \nabla_{\vec{p}} is the derivative with respect to all parameters
\vec{p}. The function therefore returns a vector of length len(p)
containing the Jacobian evaluated at the given values of \vec{p} and
\vec{x}.