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