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Re: On errors calculated by curve-fitting routines [message #59170 is a reply to message #59078] Sat, 08 March 2008 10:27 Go to previous messageGo to previous message
Craig Markwardt is currently offline  Craig Markwardt
Messages: 1869
Registered: November 1996
Senior Member
Gernot Hassenpflug <gernot@nict.go.jp> writes:
> I'd just like to ask, since I cannot quite tell if I have grasped the
> ideas from Numeric Recipes correctly (and so my own IDL code for
> comparison with the others may be incorrect): the covariance matrix
> calculation uses the basis functions (e.g., 1, x, x^2) and the
> variances of the dependent (y) variable, but *not* the dependent
> variable itself nor any quantitative measures of the goodness of the
> fitting process (presumably the variances of the dependent variable
> are supposed to contain all such information in theory).

That is the formal definition of the covariance matrix, assuming the
measurement uncertainties are appropriate.

> I ask this because other methods, such as that used by Maple, seem to
> scale their result by the residual sums of squares, for example. I am
> still awaiting the book by Bevington (can only get 1st edition from
> library services, so need to purchase 2nd edition) and the one by
> Himmelblau from 1970 which is the basis of the Maple method.

This approach *could* be appropriate. The reasoning is that although
the fit is formally of bad quality -- indicated by a statistically
unacceptable chi-square value -- you *assume* that the fit is good.
You do this by multiplying the uncertainties by SQRT(CHI^2 / DOF),
which produces a modified reduced chi-square value of 1. That may not
always be appropriate, and it depends mostly upon scientific
judgement.

Craig

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