# Template Profile likelihood fit using morphed histograms

Dear Roofit community,

I would like to implement profile likelihood template fit, but I am not really sure how to do this or if it is possible within roofit and roostats. The idea is simple, I have different histograms for different top quark widths (of course, this is not important, the idea is to make universal profile likelihood template fit) and set of histograms for systematically shifted distributions for the nominal top quark decay width. I would like to interpolate between the discrete values of width using template morphing to obtain continuous parametrization for top width. Then I would like to extract the most probable value for this new continuous parameter representing top quark width as the only point of interest while profiling all other parameters (including normalization of signal).

I found this tutorial on how to use morphing: https://root.cern.ch/root/html/tutorials/roofit/rf705_linearmorph.C.html

And also this tutorial on how to use profiling: https://root.cern.ch/root/html/tutorials/roofit/rf605_profilell.C.html

What I don’t know is how to combine these two, is it possible? Let’s say I have three histograms (TH1) from three different width values and one up and down variation for systematics. Can you help me with the implementation, or can you point me to some example code?

Thanks and cheers,
Tomas

HI Tomas,

You can use the provided example to interpolate between histograms, but probably the best solution for you is to build a RooFit model using histograms representing nominal values and +/- 1 sigma variations. In this way you build a model as function of various parameters and then you can profile some of these parameters and have a profile likelihood as function only of your parameter of interest.
This can be easily done using the HistFactory package of Root/RooStats.
See https://cdsweb.cern.ch/record/1456844
and also the histfactory tutorials,
tutorials/histfactory

Best Regards

Lorenzo

Hi Lorenzo,

thank you very much for your answer. I understand using +/- 1 sigma variations for my systematic uncertainties. My problem is that I cannot make +/- 1 sigma variations for the parameter of interest (top quark decay width). In our previous measurements we actually used 55 different templates for width. That’s why I think I need to somehow parametrize the templates and so I thought about using morphing. The problem is I don’t know how to combine the morphings between different templates to have just one parameter for the whole range of my templates and I don’t know how to provide the output of the morphing (histograms parametrized with a continuous parameter) to the likelihood. Is this even possible?

Cheers,
Tomas

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