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Re: NonlinearModelFit on correlated data

• To: mathgroup at smc.vnet.net
• Subject: [mg104936] Re: NonlinearModelFit on correlated data
• From: Ray Koopman <koopman at sfu.ca>
• Date: Fri, 13 Nov 2009 05:58:17 -0500 (EST)
• References: <hdgq0d$i77$1@smc.vnet.net>

Shouldn't your chisquare (in Mathematica notation)
be (y-f).Inverse[covariancematrix].(y-f)?
Try NMinimize on the mathematically equivalent
but computationally better expression (#.#&)[(y-f).u],
where u = Inverse@CholeskyDecomposition[covariancematrix].

On Nov 12, 3:02 am, L.J.A.Vasq... 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,
> --
> Louella
> __________________________________
> Louella Judy A. Vasquez
> Department of Physics and
> Centre for Scientific Computing
> University of Warwick, Coventry CV47AL
> United Kingdom
>
> PHONE:  +44 (24) 765 74309
> MOBILE:  +44 790 4336687