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Calculating parameter uncertainty #72
Description
At the end of a parameterization, we should calculated the "uncertainty range" for each parameter. This is currently done manually, by taking the 1st and 2nd derivatives of the score with respect to each parameter, assuming it's a harmonic function, and calculating which parameter change (backwards and forwards) will bring the score past an approximate threshold (for example, 0.1% increase, but this should be an input parameter). Preferably, this should be done internally, and listed together with the 1st and 2nd derivatives. Note that the equation requires you to know the differentiation step for each parameter.
We should report these ranges when we publish new force fields (we haven't always done that). Also, these ranges can be used for some important testing. If, for example, a torsional parameter range includes zero, the parameter should generally be set to zero and the remaining parameters reoptimized.