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January 24th, 2012, 05:22 AM   #1
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Goodness of fit metrics for comparing non-linear data series

Apologies if this is an inappropriate place to post my question.

I have ~650 concentration vs time profiles where dt increases in an irregular manner with t.

The values of a subset of the parameters that I believe dictate the shape of this profile are known.

A model of the underlying process exists. This model can be supplied with known parameter values and parameter estimates to produce
simulated concentration profiles (with v. small dt) that can be compared to real profiles. Expressing this model algebraicly will not be trivial, if possible at all. It is presently evaluated in an iterative manner.

The real and simulated concentration profiles look very approximately like exp(-x) for x < a value and like 1-exp(-x) for x >= that value.

I wish to find a goodness of fit metric that allows me to compare a real concentration profile to a corresponding simulated one, preferably one that is suitable for application to non-linear data (unlike the least-squares error) and is somewhat 'shape-aware' i.e. a 'soft' metric.

Any suggestions?

(The end goal is to find a method for identifying the most likely theoretical concentration profile given a sparse and noisy real profile.)

Regards,

Will Furnass
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