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Re: Possible inconsistency in gsl_multifit_covar
- From: Brian Gough <bjg at network-theory dot co dot uk>
- To: Giulio Bottazzi <giulio dot bottazzi at libero dot it>
- Cc: gsl-discuss at sources dot redhat dot com
- Date: Tue, 23 Aug 2005 15:29:29 +0100
- Subject: Re: Possible inconsistency in gsl_multifit_covar
- References: <20050821010321.56bc297e.giulio.bottazzi@libero.it>
Giulio Bottazzi writes:
> I've noticed that the matrix returned by the
> function "gsl_multifit_covar" is defined as
>
> (J^T J)^{-1}
>
>
> Now the problem is that this matrix IS NOT the
> (approximated) estimated variance-covariance matrix of the asymptotic
> normal distribution of the estimates. This should indeed be defined as
>
> \sigma^2 (J^T J)^{-1}
>
Hello,
The multifit functions are a translation of the corresponding MINPACK
routines, which defined 'covar' as in GSL. In MINPACK the definition
of J includes a factor of sigma
J_ij = dF_i/dx_j
F_i = (y_i-y(x))/sigma_i
Does this account for the difference above?
--
Brian Gough