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Re: NonlinearModelFit on correlated data

• To: mathgroup at smc.vnet.net
• Subject: [mg104911] Re: [mg104861] NonlinearModelFit on correlated data
• From: Darren Glosemeyer <darreng at wolfram.com>
• Date: Fri, 13 Nov 2009 05:53:31 -0500 (EST)
• References: <200911121102.GAA18623@smc.vnet.net>

L.J.A.Vasquez at warwick.ac.uk wrote:
> Hello.
>
> I want to perform a nonlinear model fitting on data points with some
> significant correlations in them.
> For these correlated data points, the definition of chi^2 is
>
> chi^2=Sum_i  Sum_j  [ y_i - f(y_i) ] * [ y_j - f(y_j) ] / Covariance(y_i,
> y_j) .
>
> Currently, I am using the Mathematica function "NonlinearModelFit" which
> unfortunately only  assumes statistically independent data points and does
> not allow to incorporate correlation in the data points when estimating
> the best fit parameters.
>
> I have looked at other data fitting functions such as FindFit and even
> GeneralizedLinearFit but i haven't found one yet that takes into account
> correlated data.
>
> Maybe i am missing something.  Is there a way to perform a nonlinear fit
> for a correlated data points? Is there a way to change how the chi^2 is
> being defined in any of the Mathematica fitting function? Perhaps, there
> is an additional Mathematica package that is available and deals with this
> problem.  Any help is most welcome.
>
> With my best regards,
>   

You could try approaching this as a direct optimization problem. One way 
to do that is to construct the chi^2 expression and use FindMinimum or 
NMinimize to minimize the chi^2 to obtain parameter estimates.

Darren Glosemeyer
Wolfram Research

• References:
  • NonlinearModelFit on correlated data
    • From: L.J.A.Vasquez@warwick.ac.uk