Weeds: Modeling weed density over time
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The goal of this problem is to model weed density from 12 years of
data in the form of an S-shaped curve. The data are simply 12 densities
at equispaced index times. The suggested model was a three-parameter 
logistic function, though an extension to estimate the variance 
around the model is also of interest.

The problem is relatively difficult, especially in its original presentation,
as it is badly scaled and there are nearly flat areas of the sum of squares or
likelihood surface. Moreover, the Hessian at the solution is effectively
singular, so methods based on Newton's iteration do rather badly, while
crude approaches such as Nelder-Mead may do better if they can be scaled
appropriately.

author: John C. Nash and Anders Nielsen and Ben Bolker