document polydispersity and fitting for integer parameters

[pkienzle]

Models with integer parameters can use array polydispersity to get an instant mixture model across different n. This should be documented in fitting/media/pd_help.rst.

For larger n, continuous distributions can also be used. This should be documented in the same place, along with the caveats on using them.

Elsewhere in the fitting documentation, we need suggest ways of fitting integer parameters. DREAM should work well enough. DE and Nelder-Mead may also work. Newton methods will fail.

[richardh]

Agree with all of the above.
However though array polydispersity can compute any combination of small numbers of layers in say a multilayer vesicle it won't actually fit the distribution.
The nice way to do this would be to be able to fit the values in the array distribution.

The messy, but existing, way is to set up a sum of n=1,2,3,4 models and fit the scale parameters! However that then needs say constraints to tie all the shell thicknesses together within the summed model, and I don't know that that works properly!

Fitting the values in the array distribution can also be applied to continuous orientational or size polydispersity, where you can interpolate a smooth distributuion between a few points being fit in an arbitary shape array (Likely best with a smoothness constraint and forcing it to zero at large & small sizes). FISH does this for arbitrary size distributions, though it is a bit tricky to set up and good convergence is tedious to find when there are a lot of wiggles in the data, though DREAM might do much better.

For broader, fairly smooth size distributions a sum of two or three Schultz or Gaussians actually works quite well.

[pkienzle]

See also #882.