[Ifeffit] What confidence limit is implied in the error bars for least-squares fitting in Athena
Matt Newville
newville at cars.uchicago.edu
Thu Oct 2 17:34:08 CDT 2008
> Athena uses Ifeffit's minimize function. As you say, the data
> uncertainty is set to one, so the diagonals of the covarience matrix
> will be orders of magnitude too small. My understanding is that
> Ifeffit rescales the error bars on the variable parameters in the same
> manner as the feffit function does -- that is, by the square root of
> reduced chi-square.
>
> In that case, the error bars are reported are 1-sigma error bars given
> the assumption that the fit is, in fact, a good fit.
>
> Or do I not understand what minimize is doing? Or are there too many
> possible meanings of the word "sigma" in this context such that we are
> talking about different things?
>
Yes, that is all correct (and the reference manual is no doubt
confusing!!) It asserts the fit is good (and that all the data points
are independent), and so asserts the uncertainty in the data is the
typical misfit of data-model. And with that estimate, it reports
1-sigma uncertainties in the parameters.
But that's not using an actual estimate of sigma from the data (unless
explicitly provided). So the value of chi-square is not scaled
correctly.
--Matt
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