Data-free estimation algorithms

A great deal has been written about the optimality of the krlglng estimates and about the error characterization provided by Iso-varlance maps such as that of Figure 1. However, krlglng, and more generally data-free estimation algorithms, have several drawbacks. 

Various rate equations have been considered to fit the experimental data. The kinetic parameters involved in the equations have been estimated by means of a derivative-free minimisation algorithm, in order to compare the different models with respect to the sum of... 

The two last points, of course, apply to any numerical method to compute energy or forces for the Coulomb or dipolar sum. Error estimates can tell us if we might see artifacts in simulations due to too small cutoffs, or if our observations have some other origin. They can tell us how the algorithm scales at its optimal point and they can help us save a lot of expensive computer time. Unfortunately, some of the free or commercially available computer programs choose parameter combinations automatically, according to some more or less known rules. Often, the user is not aware of the applied approximations, which is a very dangerous route, since, after all, one needs to interpret the data. Therefore, we stress here the point that for all our implemented routines where we have error estimates, we make use of them. 

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