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I note that in the 'more info' for NonlinearModelFit it says that it assumes the values are normally distributed around the mean response function y, which I understand is required if one wants to use maximum likelihood methods and construct confidence intervals etc.

However, there appears to be no such mention in FindFit, and my understanding (which may be way off) is that Gaussian residuals isn't so important if you want to estimate parameters, only if you want to do confidence/inference stuff.

Is this correct? If so, why when I transform my function (and data), do a fit and then transform back, do i get different parameter values compared to just fitting the 'naked' untransformed model and data? Is this due to some artefact of the algorithm (in this case NMinimize) being used, or is it a deeper issue? Is there not a one to one mapping of the sum of the squared residuals, and the parameters that minimize them?

Thanks in advance!

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# [Mathematica] FindFit/NonlinearModelFit with non-gaussian residuals

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