Gaussian constraint in `normfactor` - pyhf

Question

I would like to understand how to impose a gaussian constraint with central value expected_yield and error expected_y_error on a normfactor modifier. I want to fit observed_data with a single sample MC_derived_sample. My goal is to extract the bu_y modifier such that the integral of MC_derived_sample scaled by bu_y is gaussian-constrained to expected_yield +/- expected_y_error.
My present attempt employs the normsys modifier as follows:
spec = {
"channels": [
{
"name": "singlechannel",
"samples": [
{
"name": "constrained_template",
"data": MC_derived_sample*expected_yield, #expect normalisation around 1
"modifiers": [
{"name": "bu_y", "type": "normfactor", "data": None },
{"name": "bu_y_constr", "type": "normsys",
"data":
{"lo" : 1 - (expected_y_error/expected_yield),
"hi" : 1 + (expected_y_error/expected_yield)}
},
]
},
]
},
],
"observations": [
{
"name": "singlechannel",
"data": observed_data,
}
],
"measurements": [
{
"name": "sig_y_extraction",
"config": {
"poi": "bu_y",
"parameters": [
{"name":"bu_y", "bounds": [[(1 - (5*expected_y_error/expected_yield), 1+(5*expected_y_error/expected_yield)]], "inits":[1.]},
]
}
}
],
"version": "1.0.0"
}
My thinking is that normsys will introduce a gaussian constraint about unity on the sample scaled by expected_yield.
Please can you provide me any feedback as to whether this approach is correct, please?
In addition, suppose I wanted to include a staterror modifier for the Barlow-Beeston lite implementation, would this be the correct way of doing so?
"samples": [
{
"name": "constrained_template",
"data": MC_derived_sample*expected_yield, #expect normalisation around 1
"modifiers": [
{"name": "BB_lite_uncty", "type": "staterror", "data": np.sqrt(MC_derived_sample)*expected_yield }, #assume poisson error and scale by central value of constraint
{"name": "bu_y", "type": "normfactor", "data": None },
{"name": "bu_y_constr", "type": "normsys",
"data":
{"lo" : 1 - (expected_y_error/expected_yield),
"hi" : 1 + (expected_y_error/expected_yield)}
},
]
}
Thanks a lot in advance for your help,
Blaise