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