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NonlinearModelFit on correlated data

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104861] NonlinearModelFit on correlated data
  • From: L.J.A.Vasquez at warwick.ac.uk
  • Date: Thu, 12 Nov 2009 06:02:04 -0500 (EST)

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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