Commit b6d6429e697b866d568b8ccc89be001d7d10a619
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doc/source/users/user_manual/likelihood.rst
| @@ -177,14 +177,9 @@ Levenberg-Marquardt algorithm | @@ -177,14 +177,9 @@ Levenberg-Marquardt algorithm | ||
| 177 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ | 177 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
| 178 | 178 | ||
| 179 | ctools uses an iterative Levenberg-Marquardt algorithm for maximum likelihood | 179 | ctools uses an iterative Levenberg-Marquardt algorithm for maximum likelihood |
| 180 | -estimation. Since the Levenberg-Marquardt algorithm minimizes a function, we | ||
| 181 | -use | ||
| 182 | - | ||
| 183 | -.. math:: | ||
| 184 | - f(M) = -\ln L(M) | ||
| 185 | - | ||
| 186 | -as the function to minimize by the algorithm. The Levenberg-Marquardt algorithm | ||
| 187 | -starts with an inital guess of the :ref:`model <um_models>` parameters | 180 | +estimation. Since the Levenberg-Marquardt algorithm minimises a function, we |
| 181 | +use :math:`-\ln L(M)` as the function to minimse. The Levenberg-Marquardt | ||
| 182 | +algorithm starts with an inital guess of the :ref:`model <um_models>` parameters | ||
| 188 | :math:`a_k` and iteratively replaces this estimate by a new estimate | 183 | :math:`a_k` and iteratively replaces this estimate by a new estimate |
| 189 | :math:`a_k + \Delta a_k`. The :math:`\Delta a_k` are determined by solving | 184 | :math:`a_k + \Delta a_k`. The :math:`\Delta a_k` are determined by solving |
| 190 | 185 |