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After solving the inverse problem*, how to investigate whether the solution is unique or not? When I check theoretical values and published values during the convergence and search for the lowest value for chi-squared, is it sufficient?

*The task when the observed data is given (radial velocity, light curves for an eclipsing binary), and someone needs to determine the set of parameters for which the model yields the best match of the observed curves.

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  • $\begingroup$ I think you mean "when identifying the causes of a set of observations"... "how to I determine if my solution is unique. Is that right? $\endgroup$
    – James K
    Aug 30 at 7:20
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    $\begingroup$ I mean that the observed data is given (radial velocity, light curves for an eclipsing binary), and someone needs to determine the set of parameters for which the model yields the best match of the observed curves. $\endgroup$
    – Anna-Kat
    Aug 30 at 7:21
  • $\begingroup$ @JamesK yes it is right $\endgroup$
    – Anna-Kat
    Aug 30 at 7:24
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    $\begingroup$ In general you can't. An method based on convergence can hope at best to find a local minimum (of chi-squared or however you are judging the goodness of fit) There might be other, better minima that your method doesn't find. $\endgroup$
    – James K
    Aug 30 at 7:25
  • $\begingroup$ So the only inspection is to try whether slightly different initial values led to a similar solution and check that the resulting values make sence, right? $\endgroup$
    – Anna-Kat
    Aug 30 at 7:28

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