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From: L.J.A.Vasquez on 12 Nov 2009 06:02
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

From: Darren Glosemeyer on 13 Nov 2009 05:54
L.J.A.Vasquez(a)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

From: Ray Koopman on 13 Nov 2009 05:58
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(a)CholeskyDecomposition[covariancematrix].

On Nov 12, 3:02 am, L.J.A.Vasq...(a)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

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