Dispersion parameter grid search

One of the most statistically unbiased methods for determining an initial parameter estimate prior to optimisation is to perform a grid search. This is performed via the minimise.grid_search user function (see Section 17.2.70 on page ).

For some dispersion models the grid search can be too computationally expensive. In this case, some tricks can be used to bypass the parts of the grid search or the whole grid search:

Model nesting:: Using the optimised parameters of a simpler nested model as the starting point for optimisation.
Model equivalence:: Using the optimised solution of an equivalent analytic model as the starting point for a numeric model.

These tricks are implemented in the relaxation dispersion auto-analysis protocol as described above. If you do not use the auto-analysis or the GUI, then you are free to implement your own solutions.

The grid search lower and upper bounds default to:

$\begin{subequations}\begin{gather} 5 \leqslant \mathrm{R}_2^0\leqslant 20, \\ 5... ... 1e^{-4} \leqslant \tau_{\textrm{ex}}\leqslant 1. \end{gather}\end{subequations}$

For the MMQ models, the grid bounds are slightly different with

$\begin{subequations}\begin{gather} -10 \leqslant \Delta\omega \leqslant 10, \\ ... ...tscriptstyle\mathrm{H}}_{\textrm{BC}}\leqslant 3. \end{gather}\end{subequations}$

These values can be changed when not using the auto-analysis. Linear constraints can decrease the number of grid points searched through.

The relax user manual (PDF), created 2020-08-26.