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Trying to fit a model (bloch equations from MRI) to experimental data (12 parameters, 12 equation). Monte Carlo Multistart ('lsqcurvefit' in MATLAB) gives expected values for all parameters except for two, which are correlated:

http://imgur.com/1PRayGj

Briefly about the model. It is a system of differential equations (solved numerically by Cramer's rule). The fig. contains 9 diff. eq. My model is a bit more complicated and contain 12 diff. eq.

enter image description here

![http://imgur.com/E5LiYdq] (the model)

I am passing initial guess, lower and upper bounds for all parameters to the solver. 1st parameter always takes the value of its upper limit and 2nd one the value of its lower limit (please, see the fig.).

Bad luck, because I am only after those two parameters. Are there any good fitting algorithm for correlated data?

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    $\begingroup$ Might help if you explain what kind of model you're trying to fit. $\endgroup$
    – John
    Jan 21, 2014 at 14:39
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    $\begingroup$ More details would indeed be necessary. One thing that might work depending on the situation is too make some strong structural assumption, e.g. impose priors on the parameters if there is any trustworthy knowledge you can draw upon. $\endgroup$
    – Erik
    Jan 21, 2014 at 14:57
  • $\begingroup$ Sorry, just added more details. I hope now it is more clear. Thank you for your time. $\endgroup$
    – Alex
    Jan 21, 2014 at 15:34
  • $\begingroup$ That helps, but this question is still too vague. For instance, you don't even mention which specific parameters you are concerned about, you do not describe how your plot was produced (it certainly is not a plot of correlation), nor do you describe what procedure you are using for fitting ("numerically using Cramer's Rule" is not only vague, but puzzling). Information about all these would be helpful, because there is no universal procedure for solving complex nonlinear problems like this. $\endgroup$
    – whuber ♦
    Jan 21, 2014 at 16:22

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