Errordef value when using iMinuit as minimiser

[reallyblaised]

Hello experts,

I just wondered if in a scenario of a binned maximum likelihood fit with pyhf and iMinuit as minimiser, I must manually modify the errordef to counteract potential factors of 2, or whether this is automatically taken care of in defining the likelihood internally.

Pragmatically, I was wondering whether I should use this snippet at the start of my fitting code:

  pyhf.set_backend(
    # https://scikit-hep.org/pyhf/_generated/pyhf.optimize.opt_minuit.minuit_optimizer.html
    # 0.5 errordef for NLL
    "numpy",
    pyhf.optimize.minuit_optimizer(verbose=1, errordef=0.5),
    )  # get uncertainties and covariance
    pyhf_fit_result, result_obj = pyhf.infer.mle.fit(
        data, pdf, return_result_obj=True, return_uncertainties=True
    )

to extract the correct error estimate. I have seen related differences in other discussions, but I thought it useful to confirm this once and for all.

Thanks a lot in advance!

[alexander-held]

Hi, this relates back to #1006. Currently pyhf uses 2*NLL as objective function to minimize:

pyhf/src/pyhf/infer/mle.py

Lines 132 to 134 in e8789a2

	return opt.minimize(
	twice_nll, data, pdf, init_pars, par_bounds, fixed_vals, **kwargs
	)

With this definition, errordef=1 is the correct thing to use, which is what pyhf does internally as well:

pyhf/src/pyhf/optimize/opt_minuit.py

Line 41 in e8789a2

self.errordef = kwargs.pop('errordef', 1)

There is no need to manually change errordef. If pyhf changes to the NLL as objective, the errordef would have to also be changed at the same time. If you run the fit externally, the right value depends on what you use as objective. You can do 0.5 and NLL or 1.0 and 2*NLL (or in principle any other multiple of those).