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Understanding fitting results


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What if my run never finishes?

What if the parameter hits a limit in a 'fit-only' run (using an algorithm that honors the limits: GlobalSearch, MultiStart, or DirectSearch).

What if I see some parameters extremely tightly correlated in Monte-Carlo?



A sum of squares of the best-fit to the experimental data larger than any of fits to the simulated Monte-Carlo ensemble

Random perturbation (Monte Carlo, MC) of simulated data is intended to simulate variability in real data. Fitting of these MC datasets produces model parameters that correspond to differently perturbed data. Their best-fit values from multiple MC runs are represented as histograms (below, top panel). The bottom panel on the graph shows actual value of sum of squares for all of the runs included in the histogram (shown as black dots). The sum of squares of the best fit to the original experimental data is shown as a red dot. If we correctly take into account all sources of uncertainty in the experimental data and the perturbation we apply to the simulate "noisy" data is adequate---the red dot will reside inside a cloud of black dots.

However, if sum of squares of best fit to the experimental data is larger than SS of MC sets---red dot is well above black dots---this is an indication that (1) model curve does not go through the data, and (2) perturbation used to produce "noisy" datasets for Monte-Carlo analysis is inadequate by being too small or not taking into account some significant source of uncertainty. This results in ensemble of simulated datasets in the Monte-Carlo analysis being a poor mimic of experimental data. In this case uncertainties of best-fit parameters determined from the MC ensemble are meaningless!

The reason for the case above is that the curves do not go through the data quite well due to large noise (distortions) in experimental data (graph below). The error bars shown on experimental curves were derived from some instrumental measurement of noise. Obviously, these data contain additional unaccounted source of experimental error or the instrumental error measurement is underestimation.

For comparison, the example of the fit that adequately goes through the data is shown below. This fitting session that produced the very first graph in the beginning of this section, where best-fit SS (red dot) is well within the simulated "noisy" MC ensemble (black dots).