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    $\begingroup$ This is a nice approach -thank you. I have added your plots (which will only appear when peer reviewed). I regret I don't agree with your analysis. The plots for model 1 look nice and quadratic (as I suggested in the second part of my question). The plots for model 2 are wild and could easily take you off in the wrong direction. I would suggest that the comments you made can be reversed. The issue of parameters being of the same order of magnitude is one I will think about. $\endgroup$ Commented Aug 28, 2015 at 17:07
  • $\begingroup$ A very clear demonstration of going in circles. I wonder if this is almost a bug because it should be detectable and I would imagine there is a work around. The point about the phase is worth further thought. The result should be periodic in phase so there are parallel good valleys and it will not matter which one you are in. Thanks $\endgroup$ Commented Aug 31, 2015 at 15:43
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    $\begingroup$ @Hugh At other occasions Mathematica detects oscillatory behaviour, so it should be possible here as well. Overall, I think this is a good example that making a proper transformation of parameter space can remove pathological behaviour and result in much better conversion. The idea is to decouple the parameters and make things orthogonal such that you get a proper parabolic minimum. $\endgroup$ Commented Aug 31, 2015 at 16:30
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    $\begingroup$ I agree about trying to find a good parameter space. The counterintuitive part is that it is better to have two nonlinear parameters and one linear rather than two linear and one nonlinear. I had thought that the more linear parameters the better but that is wrong. I wonder if the final polishing is in a quadratic well. $\endgroup$ Commented Aug 31, 2015 at 16:36
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    $\begingroup$ What? No buttocks? $\endgroup$ Commented Sep 1, 2015 at 17:03