Re: how to re-calculate error matrix in TMinuit

Hello,

you can apply the error propagation.

Given a set of functions y(i) = f_i(x) which transform your variables x -> y
you can build the derivative matrix of this functions (evaluated at the minimum x value):

A(i,j) = df_i/dx_j

and then the new covariance matrix will be

U = A V At where At is the transpose of A and V is the original covariance matrix.

This procedure assumes that the functions f_i can be well approximated by the first-order Taylar expansion around the minimum value ( to a scale of the order of sigma). If this is not the case, i.e. in the presence of very non-linear functions, I would perform a new minimization with the new variables and re-run Minos.

Best Regards,

  Lorenzo

On 12 May 2007, at 10:54, X. Lu, Peking Univ. wrote:

> Dear Rooter,
>
> I have the following question about TMinuit:
>
> I have performed a Maximum Likelihood fit using TMinuit, and
> obtained estimated parameters and errors.
> Then I want to get a new error matrix by changing some variables
> (such as weight) at the found minimum of the -log likelihood function.
> How can I do this without performing a new minimization procedure
> of TMinuit ?
>
> Thanks in advance !
>
> Best Regards,
> Xianguo
>
> --
> Take flight into the sky, beyond the moon, beyond my mind.
>
> Xianguo LU
> Physics Department, Peking University
> Beijing, China
> Tel: 0086-10-62753888(o)
Received on Sun May 13 2007 - 21:25:04 CEST