# Relation between FCN value at minimum and EDM

Hi

I have 2 questions.

1. Does minuit stop if the value of my chi2 is <= edm? Then, the weights I use in the chi2 are critical and leaving them equal to 1 may not be very useful. Should I modify the value of edm (via the tolerance parameter) or is it something I should not touch?

2. I am using a simulation to test a fitting program. So I generate a simulation out of know parameters. Then I use the same simulation (starting from values different to the true ones) to guess the parameters. What should I use as weights for the chi2 in this case?

Thank you

Hi,

1. The minimisation will stop if the edm (expected distance form the minimum) is less than the given tolerance and it has noting to do with the value of the chi2. The only thing is that having absolute chi2 values around 1 or closer is often better for numerical precision.

2. The weights to use in the chi2 should be of the order of the inverse error of your chi2 residuals. Optimally each chi2 element should follow a normalized gaussian distribution (normal with mean=0 and sigma=1).

Best Regards

Lorenzo

Dear Lorenzo,

thank you very much for your answer! I would like to follow a bit more on this…

1. If the EDM does not refer to the value of chi2, then, EDM is the distance to which minimum? I thought minuit was trying to find the position of the minimum of the chi2 that I calculate.

2. I am fitting simulated data from which I know all the parameters. I ran a fit 7 times, each time with a different (but constant) weight. I varied the weight from 1 to 1.e-7. The fit contains 200 points. I have realised that I get the right parameter values if weight=1.e-3. For all other weights, the calculated parameters are wrong. Since the weights are constant, I expected the shape of the chi2 to be the same. Shouldn’t minuit arrive always to the same minimum??

Thank you

1. See eq. 4.2 in seal.web.cern.ch/seal/documents/ … torial.pdf for the definition of the EDM.

2. Changing the weight change the shape of the chi2. Around the minimum the parabola will be steeper or broader by changing the weight. However a change of a constant weight should not change the location of the function minimum.
If it changes it means that the starting minimisation point is not optimal and in some case the convergence to the correct minimum is not reached. Maybe the minimisation gets stack in a local minimum.

Lorenzo