how to set one fitting parameter larger than the other as constraints in iminuit in python?

Question

I have two related fitting parameters. They have the same fitting range. Let's call them r1 and r2. I know I can limit the fitting range using minuit.limits, but I have an additional criteria that r2 has to be smaller than r1, can I do that in iminuit?

Answer 1

I've found this, I hope this can help you!

Extracted from: https://iminuit.readthedocs.io/en/stable/faq.html

**Can I have parameter limits that depend on each other (e.g. x^2 + y^2 < 3)?**¶ MINUIT was only designed to handle box constrains, meaning that the limits on the parameters are independent of each other and constant during the minimisation. If you want limits that depend on each other, you have three options (all with caveats), which are listed in increasing order of difficulty:

Change the variables so that the limits become independent. For example, transform from cartesian coordinates to polar coordinates for a circle. This is not always possible, of course.

Use another minimiser to locate the minimum which supports complex boundaries. The nlopt library and scipy.optimize have such minimisers. Once the minimum is found and if it is not near the boundary, place box constraints around the minimum and run iminuit to get the uncertainties (make sure that the box constraints are not too tight around the minimum). Neither nlopt nor scipy can give you the uncertainties.

Artificially increase the negative log-likelihood in the forbidden region. This is not as easy as it sounds.

The third method done properly is known as the interior point or barrier method. A glance at the Wikipedia article shows that one has to either run a series of minimisations with iminuit (and find a clever way of knowing when to stop) or implement this properly at the level of a Newton step, which would require changes to the complex and convoluted internals of MINUIT2.

Warning: you cannot just add a large value to the likelihood when the parameter boundary is violated. MIGRAD expects the likelihood function to be differential everywhere, because it uses the gradient of the likelihood to go downhill. The derivative at a discrete step is infinity and zero in the forbidden region. MIGRAD does not like this at all.