# How to rescue the unsatisfied limit setting analysis?

Hi, Lorenzo (Rooters),

Let me first post a limit setting plot here(The error bars are quite big due to the small number of toys, 100/50 in order to save running time).
Apparently, no blue points going below 90% CL line.

The following plot is profile likelihood ratio, which shows the profile likelihood s+b can’t converge, and their shapes are almost exactly same in all different POI values.

There exist at least two problems for the fit I think.
1). why the s+b can’t converge ?
In my analysis, the model and data are obtained independently.
Here is exactly the key question I’d like to ask : to set a limit, is mandatory to require a model fit the data well or not ? Given the model and data are both there already, how to obtain satisfied limit analysis ?

2). why the p values of “s+b” are so stable ?
After checking the related documents on websites, I found on the slide 27 of your presentation at Terascale statistics school 2015, there is one line says, “pdf are normalized over allowed range of observables x with respect to the parameters p”.
Does this mean if a model depends on a POI in a scalable way, the test statistics can’t tell the difference of the models with different POI values ? Therefore, the blue points are a kind of stable at p value = 0.55 ?
BTW, = (POI)^2 * .
For example, these two plots are my signal models corresponding to different POI values. The shape of these two models are exactly same, the only difference are the magnitudes.

In this case, can RooFit tell the difference of two models ?

Best,
Junhui

Hi,

I see first of all from your plots that you have many negative test statistics values which are negative. This can be caused by failing fits, because the minimum of the likelihood is larger than the likelihood computed at the given POI value. This means that the minimum is not really a minimum !
I don’t know why this is happening, maybe because the model is not fully corrected defined (e.g. having too many correlations, pdf not computed correctly numerically, etc…)

Concerning the second point, if your POI has an effect only on the normalisation, this should not go away
(if your model is correctly defined). Your likelihood fit should be extended, i.e. the likelihood should have a poisson term describing the total number of observed events given the total expected ones.

Best Regards

Lorenzo

Hi, Lorenzo,

The following plot is the pdf generated by RooFit(by “cout” part of the values of the pdf).

The next plot is a signal model provided by a mathematica script.

I guess these two plots are enough to demonstrate the signal PDF has been generated correctly by RooFit.
(BTW, these two plots are different than the two in my first posts because there is an improvement here).
Given the signal PDF shown above, do you think how “difficult” for RooFit to find the correct minimum if the likelihood is based on the PDF ?

Besides, I’d like to attach the data to be analyzed and an exponential fit(red curve) to the data.

I’m taking the fit curve as the pdf of background because the number of signal events is supposed to be < 1.

Indeed, the likelihood contains an extended Poisson.
However, I’d like to ask on this : according to the model, the number of events is supposed to be less than 1.
So, the likelihood I have set is :

``SUM:model([0,1]*signal_pdf, [N-1,N]*background_pdf)``

where N is the number of observed events in our data histogram, in this case is 198. Do you think is this correct ?

Do you have any other comments ?

Thanks again !

Best,
Junhui

Hi,

There should be no particular problem to find a minimum of the likelihood, if you start in the right region, so with initial parameters not too far away.

For the description of your model, the constraints NSignal < 1, seems to me very strong and could cause problems when fitting. Also you should not mix number of observed events with expected one. So, even if you want to constraint signal in [0,1], nbaground should float between 0 and a larger value than N (e.g. 2 * N) to account for possible Poisson fluctuations in the observed data

Cheers

Lorenzo

Hi, Lorenzo,

I followed your suggestion : increase the range of nsig and nbkg, but doesn’t change the results much.

Also, I have printed some outputs and found many of values of the unconditional ML and conditional ML are same. For the different values, the variance of unconnd ML and cond ML are very small.
And these kinds of equivalence happens both to Null and Alt tests.
Do you have any comments on this feature ?

I copied some of them in the following.

Best,
Junhui

``````EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1424.95, cond ML = -1424.95 pll = -1.92654e-06 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1645.09, cond ML = -1645.09 pll = -1.97819e-06 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1784.41, cond ML = -1784.41 pll = -1.04294e-08 time (create/fit1/2) 0.01 , 0.04 , 0.01
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1467.36, cond ML = -1467.36 pll = -2.12703e-07 time (create/fit1/2) 0.01 , 0.04 , 0.01
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1611.78, cond ML = -1611.98 pll = -0.202786 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1493.81, cond ML = -1494.03 pll = -0.227407 time (create/fit1/2) 0.01 , 0.04 , 0.01
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1388.86, cond ML = -1388.86 pll = -1.42534e-07 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1547.4, cond ML = -1547.4 pll = -1.37822e-06 time (create/fit1/2) 0 , 0.05 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1497.9, cond ML = -1497.97 pll = -0.0639473 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1530.88, cond ML = -1530.88 pll = -2.9695e-09 time (create/fit1/2) 0 , 0.04 , 0.01
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1457.61, cond ML = -1457.95 pll = -0.33543 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1484.86, cond ML = -1484.86 pll = -1.74151e-07 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1422.59, cond ML = -1422.88 pll = -0.292332 time (create/fit1/2) 0.01 , 0.03 , 0.01
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1490.92, cond ML = -1491.07 pll = -0.149959 time (create/fit1/2) 0.01 , 0.04 , 0.01
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1487.1, cond ML = -1487.1 pll = -8.32949e-08 time (create/fit1/2) 0 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1499.49, cond ML = -1499.49 pll = -1.03323e-06 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1540.83, cond ML = -1540.83 pll = -0.00166172 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1470.25, cond ML = -1470.25 pll = -1.2597e-07 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1569.26, cond ML = -1569.26 pll = -1.29606e-05 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1541.62, cond ML = -1541.87 pll = -0.24377 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1797.61, cond ML = -1797.61 pll = -1.74889e-08 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1488.91, cond ML = -1489 pll = -0.0936852 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1747.36, cond ML = -1747.48 pll = -0.121815 time (create/fit1/2) 0.01 , 0.05 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1693.96, cond ML = -1694.22 pll = -0.262019 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1610.51, cond ML = -1610.51 pll = -2.31365e-07 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1594.54, cond ML = -1594.6 pll = -0.0606269 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1747.85, cond ML = -1747.85 pll = -0.00526239 time (create/fit1/2) 0.01 , 0.05 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1667.33, cond ML = -1667.33 pll = -3.48655e-09 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1462.14, cond ML = -1462.26 pll = -0.118133 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1674.47, cond ML = -1674.62 pll = -0.148551 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1571.61, cond ML = -1571.72 pll = -0.106181 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1669.75, cond ML = -1669.84 pll = -0.0923667 time (create/fit1/2) 0.01 , 0.04 , 0.01
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1723.34, cond ML = -1723.34 pll = -3.57213e-08 time (create/fit1/2) 0 , 0.05 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1540.48, cond ML = -1540.79 pll = -0.311868 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1700.76, cond ML = -1700.76 pll = -1.25178e-08 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1596.52, cond ML = -1596.52 pll = -5.20363e-08 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1809.66, cond ML = -1810.02 pll = -0.363933 time (create/fit1/2) 0.01 , 0.05 , 0
EvaluateProfileLikelihood - mu hat = 0.0539556, uncond ML = -1462.69, cond ML = -1462.69 pll = -5.49593e-07 time (create/fit1/2) 0.01 , 0.03 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1495.01, cond ML = -1495.01 pll = -4.67189e-06 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1500.52, cond ML = -1500.62 pll = -0.100682 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1390.18, cond ML = -1390.27 pll = -0.0849392 time (create/fit1/2) 0 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1447, cond ML = -1447 pll = -5.38332e-07 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1649.78, cond ML = -1649.89 pll = -0.108303 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1482.83, cond ML = -1482.84 pll = -0.0120152 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1269.56, cond ML = -1269.56 pll = -2.71023e-07 time (create/fit1/2) 0.01 , 0.03 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1467.11, cond ML = -1467.11 pll = -1.80545e-07 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1448.01, cond ML = -1448.12 pll = -0.102854 time (create/fit1/2) 0 , 0.04 , 0.01
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1408.75, cond ML = -1408.93 pll = -0.179063 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1580.5, cond ML = -1580.54 pll = -0.0493003 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1550.11, cond ML = -1550.14 pll = -0.0396728 time (create/fit1/2) 0.01 , 0.04 , 0.01
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1558, cond ML = -1558.2 pll = -0.201165 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1529.55, cond ML = -1529.55 pll = -1.32398e-07 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1494.77, cond ML = -1494.99 pll = -0.22595 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1517.94, cond ML = -1518.01 pll = -0.0646316 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1523.17, cond ML = -1523.17 pll = -6.06633e-10 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1490.53, cond ML = -1490.53 pll = -6.45668e-08 time (create/fit1/2) 0 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1326.22, cond ML = -1326.27 pll = -0.0464099 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1476.18, cond ML = -1476.18 pll = -2.15153e-06 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1515.28, cond ML = -1515.4 pll = -0.119278 time (create/fit1/2) 0 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1526.3, cond ML = -1526.37 pll = -0.0724035 time (create/fit1/2) 0.01 , 0.04 , 0.01
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1480.59, cond ML = -1480.59 pll = -1.4335e-07 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1622.5, cond ML = -1622.82 pll = -0.318874 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1516.98, cond ML = -1517.07 pll = -0.0884966 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1676.62, cond ML = -1676.62 pll = -2.21894e-09 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1427.98, cond ML = -1427.98 pll = -2.17144e-06 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1647.98, cond ML = -1647.98 pll = -1.96687e-06 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1446.43, cond ML = -1446.43 pll = -5.7142e-07 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1214.93, cond ML = -1214.93 pll = -5.28647e-07 time (create/fit1/2) 0 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1540.38, cond ML = -1540.38 pll = -1.42081e-07 time (create/fit1/2) 0 , 0.05 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1471.77, cond ML = -1471.77 pll = -4.63449e-05 time (create/fit1/2) 0.01 , 0.04 , 0.01
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1453.91, cond ML = -1453.91 pll = -4.10842e-07 time (create/fit1/2) 0 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1515.23, cond ML = -1515.42 pll = -0.187382 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1341.65, cond ML = -1341.65 pll = -6.51226e-05 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1663.05, cond ML = -1663.05 pll = -2.47474e-09 time (create/fit1/2) 0 , 0.05 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1746.94, cond ML = -1747.14 pll = -0.202195 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1677.29, cond ML = -1677.44 pll = -0.151512 time (create/fit1/2) 0.01 , 0.05 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1530.19, cond ML = -1530.19 pll = -1.40972e-10 time (create/fit1/2) 0 , 0.04 , 0.01
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1456.74, cond ML = -1456.82 pll = -0.0837261 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1481.6, cond ML = -1481.6 pll = -1.50405e-07 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1395.56, cond ML = -1395.56 pll = -1.06705e-07 time (create/fit1/2) 0.01 , 0.03 , 0.01
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1643.04, cond ML = -1643.04 pll = -1.77313e-06 time (create/fit1/2) 0.01 , 0.05 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1631.21, cond ML = -1631.21 pll = -6.27409e-07 time (create/fit1/2) 0 , 0.05 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1391.04, cond ML = -1391.04 pll = -2.76928e-05 time (create/fit1/2) 0.01 , 0.02 , 0.01
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1419.56, cond ML = -1419.62 pll = -0.0568417 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1682.35, cond ML = -1682.35 pll = -5.3119e-09 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1590.32, cond ML = -1590.32 pll = -4.55814e-08 time (create/fit1/2) 0.01 , 0.05 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1435.68, cond ML = -1435.78 pll = -0.097925 time (create/fit1/2) 0 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1313.51, cond ML = -1313.62 pll = -0.10937 time (create/fit1/2) 0.01 , 0.03 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1506.57, cond ML = -1506.57 pll = -1.1389e-06 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1556.24, cond ML = -1556.44 pll = -0.200925 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1523.72, cond ML = -1523.72 pll = -1.51141e-07 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1408.68, cond ML = -1408.68 pll = -2.64321e-06 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1532.25, cond ML = -1532.25 pll = -4.82032e-11 time (create/fit1/2) 0 , 0.04 , 0.01
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1559.44, cond ML = -1559.6 pll = -0.16776 time (create/fit1/2) 0.01 , 0.05 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1321.28, cond ML = -1321.28 pll = -3.08633e-07 time (create/fit1/2) 0 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1577.85, cond ML = -1577.85 pll = -2.45184e-08 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1570.02, cond ML = -1570.32 pll = -0.307264 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1560.28, cond ML = -1560.44 pll = -0.163905 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1450.83, cond ML = -1450.9 pll = -0.073724 time (create/fit1/2) 0.01 , 0.04 , 0
EvaluateProfileLikelihood - mu hat = 0.051668, uncond ML = -1481.61, cond ML = -1481.61 pll = -1.30062e-05 time (create/fit1/2) 0 , 0.04 , 0``````

Hi,

I see you get always the same best fit value (mu hat) all the time. This is also strange, each pseudo-experiment should have a different fitted value. It could be also due to a model description problem, since the pseudo-experiment are maybe not generated correctly.
Can you increase the print level and look at the full log of some of those fit ?
You could also look at the detailed output of the fit, obtained by setting the right flag in the test statistics

Best Regards

Lorenzo

Hi, Lorenzo,

I attached some of the outputs when I set print level as 2.
There are errors like the following, but I don’t understand what’s the exact meaning of these lines.

`````` MINUIT WARNING IN HESSE
============== Second derivative enters zero, param 1
MINUIT WARNING IN HESSE
============== Second derivative zero for parameter1
MNHESS FAILS AND WILL RETURN DIAGONAL MATRIX. ``````

Some of the outputs are here.

``````
POIs:
1) 0x1c48ae0 RooRealVar:: cof = 0.001  L(0.001 - 0.1)  "cof"
creating NLL 0x1c4c340 with data = 0x7fdd0931c554
Do unconditional fit
**********
**    1 **SET PRINT           0
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 cof          1.00000e-03  9.90000e-03    1.00000e-03  1.00000e-01
MINUIT WARNING IN PARAM DEF
============== STARTING VALUE IS AT LIMIT.
MINUIT WARNING IN PARAMETR
============== VARIABLE1 IS AT ITS LOWER ALLOWED LIMIT.
MINUIT WARNING IN PARAMETR
============== VARIABLE1 BROUGHT BACK INSIDE LIMITS.
2 nbkg         1.00000e+00  5.00000e-01    0.00000e+00  5.00000e+02
3 nsig         1.00000e+00  5.00000e-01    0.00000e+00  1.00000e+01
**********
**    3 **SET ERR         0.5
**********
**********
**    4 **SET PRINT           0
**********
**********
**    5 **SET STR           1
**********
**********
**    6 **MINIMIZE        1500           1
**********
MINUIT WARNING IN MINImize
============== VARIABLE1 IS AT ITS LOWER ALLOWED LIMIT.
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
MINUIT WARNING IN HESSE
============== Second derivative enters zero, param 1
MINUIT WARNING IN HESSE
============== Second derivative zero for parameter1
MNHESS FAILS AND WILL RETURN DIAGONAL MATRIX.
FCN=-1537.49 FROM MIGRAD    STATUS=CONVERGED     174 CALLS         175 TOTAL
EDM=5.37655e-05    STRATEGY= 1  ERROR MATRIX UNCERTAINTY 100.0 per cent
EXT PARAMETER                APPROXIMATE        STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  cof          1.05451e-03   5.05900e-02  -0.00000e+00  -2.27374e-13
2  nbkg         1.88233e+02   1.40909e+01   4.20939e-03   1.42414e-01
3  nsig         9.99997e+00   7.92597e+00  -2.63770e-01   1.13857e-03
ERR DEF= 0.5
**********
**    7 **HESSE        1500
**********
MINUIT WARNING IN HESSE
============== Second derivative zero for parameter1
MNHESS FAILS AND WILL RETURN DIAGONAL MATRIX.
FCN=-1537.49 FROM HESSE     STATUS=FAILED          3 CALLS         178 TOTAL
EDM=5.37655e-05    STRATEGY= 1  ERROR MATRIX UNCERTAINTY 100.0 per cent
EXT PARAMETER                APPROXIMATE     INTERNAL      INTERNAL
NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE
1  cof          5.99407e-03   5.08797e-02  -0.00000e+00  -1.52386e+00
2  nbkg         1.88233e+02   1.40909e+01   4.20939e-03   1.15950e+03
3  nsig         9.99997e+00   7.92597e+00  -2.63770e-01   1.57427e+00
ERR DEF= 0.5
EvaluateProfileLikelihood - mu hat = 0.00599407, uncond ML = -1537.49, cond ML = -1537.49 pll = 0 time (create/fit1/2) 0 , 0.06 , 0
[#0] PROGRESS:Generation -- Test Statistic on data: 0
[#1] INFO:InputArguments -- Profiling conditional MLEs for Null.
[#1] INFO:InputArguments -- Using a ToyMCSampler. Now configuring for Null.
POIs:
1) 0x1cc2470 RooRealVar:: cof = 0.001  L(0.001 - 0.1)  "cof"
reusing NLL 0x1c4c340 new data = 0x7fdd0931d7b4
Do unconditional fit
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 cof          1.00000e-03  9.90000e-03    1.00000e-03  1.00000e-01
2 nbkg         1.88350e+02  1.41000e+01    0.00000e+00  5.00000e+02
3 nsig         1.00000e+01  7.95566e+00    0.00000e+00  1.00000e+01
**********
**   28 **SET ERR         0.5
**********
**********
**   29 **SET PRINT           0
**********
**********
**   30 **SET STR           1
**********
**********
**   31 **MINIMIZE        1500           1
**********
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
MNHESS FAILS AND WILL RETURN DIAGONAL MATRIX.
FCN=-1546.09 FROM MIGRAD    STATUS=CONVERGED     107 CALLS         108 TOTAL
EDM=6.11937e-06    STRATEGY= 1  ERROR MATRIX UNCERTAINTY 100.0 per cent
EXT PARAMETER                APPROXIMATE        STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  cof          1.00009e-03   4.94991e-06  -0.00000e+00   0.00000e+00
2  nbkg         1.91021e+02   1.41667e+01   1.10086e-02  -3.02587e-02
3  nsig         1.00000e+01   2.29849e+00   1.97411e-03** at limit **
ERR DEF= 0.5
**********
**   32 **HESSE        1500
**********
MNHESS FAILS AND WILL RETURN DIAGONAL MATRIX.
FCN=-1546.09 FROM HESSE     STATUS=FAILED          5 CALLS         113 TOTAL
EDM=6.11937e-06    STRATEGY= 1  ERROR MATRIX UNCERTAINTY 100.0 per cent
EXT PARAMETER                APPROXIMATE     INTERNAL      INTERNAL
NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE
1  cof          7.01340e-03   6.00835e-03  -0.00000e+00  -1.56884e+00
2  nbkg         1.91021e+02   1.41667e+01   1.10086e-02  -2.38162e-01
3  nsig         1.00000e+01   2.29849e+00   1.97411e-03   1.57082e+00
WARNING -   - ABOVE PARAMETER IS AT LIMIT.
ERR DEF= 0.5
EvaluateProfileLikelihood - mu hat = 0.0070134, uncond ML = -1546.09, cond ML = -1546.09 pll = 0 time (create/fit1/2) 0.01 , 0.05 , 0

........

POIs:
1) 0x1cc9980 RooRealVar:: cof = 0.001  L(0.001 - 0.1)  "cof"
reusing NLL 0x1c4c340 new data = 0x7fdd09322914
Do unconditional fit
**********
**   68 **SET PRINT           0
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 cof          1.00000e-03  9.90000e-03    1.00000e-03  1.00000e-01
2 nbkg         1.88350e+02  1.41000e+01    0.00000e+00  5.00000e+02
3 nsig         1.00000e+01  7.95566e+00    0.00000e+00  1.00000e+01
**********
**   70 **SET ERR         0.5
**********
**********
**   71 **SET PRINT           0
**********
**********
**   72 **SET STR           1
**********
**********
**   73 **MINIMIZE        1500           1
**********
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
MNHESS FAILS AND WILL RETURN DIAGONAL MATRIX.
FCN=-1334.53 FROM MIGRAD    STATUS=CONVERGED     112 CALLS         113 TOTAL
EDM=1.88999e-08    STRATEGY= 1  ERROR MATRIX UNCERTAINTY 100.0 per cent
EXT PARAMETER                APPROXIMATE        STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  cof          1.00009e-03   4.94991e-06  -0.00000e+00   0.00000e+00
2  nbkg         1.65077e+02   1.32204e+01   2.22514e-03  -6.84855e-04
3  nsig         9.99998e+00   2.29848e+00  -6.85529e-05   1.16258e-04
ERR DEF= 0.5
**********
**   74 **HESSE        1500
**********
MNHESS FAILS AND WILL RETURN DIAGONAL MATRIX.
FCN=-1334.53 FROM HESSE     STATUS=FAILED          3 CALLS         116 TOTAL
EDM=1.88999e-08    STRATEGY= 1  ERROR MATRIX UNCERTAINTY 100.0 per cent
EXT PARAMETER                APPROXIMATE     INTERNAL      INTERNAL
NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE
1  cof          7.01340e-03   6.00835e-03  -0.00000e+00  -1.56884e+00
2  nbkg         1.65077e+02   1.32204e+01   2.22514e-03  -3.46587e-01
3  nsig         9.99998e+00   2.29848e+00  -6.85529e-05   1.56764e+00
ERR DEF= 0.5
EvaluateProfileLikelihood - mu hat = 0.0070134, uncond ML = -1334.53, cond ML = -1334.53 pll = 0 time (create/fit1/2) 0.01 , 0.04 , 0
POIs:
1) 0x1cc6470 RooRealVar:: cof = 0.001  L(0.001 - 0.1)  "cof"
reusing NLL 0x1c4c340 new data = 0x7fdd09323634
Do unconditional fit
**********
**   75 **SET PRINT           0
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 cof          1.00000e-03  9.90000e-03    1.00000e-03  1.00000e-01
2 nbkg         1.88350e+02  1.41000e+01    0.00000e+00  5.00000e+02
3 nsig         1.00000e+01  7.95566e+00    0.00000e+00  1.00000e+01
**********
**   77 **SET ERR         0.5
**********
**********
**   78 **SET PRINT           0
**********
**********
**   79 **SET STR           1
**********
**********
**   80 **MINIMIZE        1500           1
**********
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
MNHESS FAILS AND WILL RETURN DIAGONAL MATRIX.
FCN=-1624.81 FROM MIGRAD    STATUS=CONVERGED     112 CALLS         113 TOTAL
EDM=2.00176e-06    STRATEGY= 1  ERROR MATRIX UNCERTAINTY 100.0 per cent
EXT PARAMETER                APPROXIMATE        STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  cof          1.00009e-03   4.94991e-06  -0.00000e+00   0.00000e+00
2  nbkg         2.00073e+02   1.44808e+01   1.81829e-03  -2.18559e-02
3  nsig         1.00000e+01   2.29849e+00   4.96830e-08** at limit **
ERR DEF= 0.5
**********
**   81 **HESSE        1500
**********
MNHESS FAILS AND WILL RETURN DIAGONAL MATRIX.
FCN=-1624.81 FROM HESSE     STATUS=FAILED          3 CALLS         116 TOTAL
EDM=2.00176e-06    STRATEGY= 1  ERROR MATRIX UNCERTAINTY 100.0 per cent
EXT PARAMETER                APPROXIMATE     INTERNAL      INTERNAL
NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE
1  cof          7.01340e-03   6.00835e-03  -0.00000e+00  -1.56884e+00
2  nbkg         2.00073e+02   1.44808e+01   1.81829e-03  -2.01060e-01
3  nsig         1.00000e+01   2.29849e+00   4.96830e-08   1.57080e+00
WARNING -   - ABOVE PARAMETER IS AT LIMIT.
ERR DEF= 0.5
EvaluateProfileLikelihood - mu hat = 0.0070134, uncond ML = -1624.81, cond ML = -1624.81 pll = 0 time (create/fit1/2) 0.02 , 0.04 , 0
POIs:
1) 0x1c576a0 RooRealVar:: cof = 0.001  L(0.001 - 0.1)  "cof"
reusing NLL 0x1c4c340 new data = 0x7fdd09324354
Do unconditional fit
**********
**   82 **SET PRINT           0
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 cof          1.00000e-03  9.90000e-03    1.00000e-03  1.00000e-01
2 nbkg         1.88350e+02  1.41000e+01    0.00000e+00  5.00000e+02
3 nsig         1.00000e+01  7.95566e+00    0.00000e+00  1.00000e+01
**********
**   84 **SET ERR         0.5
**********
**********
**   85 **SET PRINT           0
**********
**********
**   86 **SET STR           1
**********
**********
**   87 **MINIMIZE        1500           1
**********
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
MNHESS FAILS AND WILL RETURN DIAGONAL MATRIX.
FCN=-1334.15 FROM MIGRAD    STATUS=CONVERGED     112 CALLS         113 TOTAL
EDM=8.48155e-08    STRATEGY= 1  ERROR MATRIX UNCERTAINTY 100.0 per cent
EXT PARAMETER                APPROXIMATE        STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  cof          1.00009e-03   4.94991e-06  -0.00000e+00   0.00000e+00
2  nbkg         1.66793e+02   1.32954e+01   1.93228e-03  -5.66827e-04
3  nsig         9.99998e+00   9.99859e+00   2.93509e-04  -2.58369e-04
ERR DEF= 0.5
**********
**   88 **HESSE        1500
**********
MNHESS FAILS AND WILL RETURN DIAGONAL MATRIX.
FCN=-1334.15 FROM HESSE     STATUS=FAILED          3 CALLS         116 TOTAL
EDM=8.48155e-08    STRATEGY= 1  ERROR MATRIX UNCERTAINTY 100.0 per cent
EXT PARAMETER                APPROXIMATE     INTERNAL      INTERNAL
NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE
1  cof          7.01340e-03   6.00835e-03  -0.00000e+00  -1.56884e+00
2  nbkg         1.66793e+02   1.32954e+01   1.93228e-03  -3.39302e-01
3  nsig         9.99998e+00   9.99859e+00   2.93509e-04   1.56831e+00
ERR DEF= 0.5
EvaluateProfileLikelihood - mu hat = 0.0070134, uncond ML = -1334.15, cond ML = -1334.15 pll = 0 time (create/fit1/2) 0 , 0.04 , 0
POIs:
1) 0x1d44b40 RooRealVar:: cof = 0.001  L(0.001 - 0.1)  "cof"
reusing NLL 0x1c4c340 new data = 0x7fdd09325074
Do unconditional fit
**********
**   89 **SET PRINT           0
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 cof          1.00000e-03  9.90000e-03    1.00000e-03  1.00000e-01
2 nbkg         1.88350e+02  1.41000e+01    0.00000e+00  5.00000e+02
3 nsig         1.00000e+01  7.95566e+00    0.00000e+00  1.00000e+01
**********
**   91 **SET ERR         0.5
**********
**********
**   92 **SET PRINT           0
**********
**********
**   93 **SET STR           1
**********
**********
**   94 **MINIMIZE        1500           1
**********
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
MNHESS FAILS AND WILL RETURN DIAGONAL MATRIX.
FCN=-1505.32 FROM MIGRAD    STATUS=CONVERGED     107 CALLS         108 TOTAL
EDM=1.60915e-05    STRATEGY= 1  ERROR MATRIX UNCERTAINTY 100.0 per cent
EXT PARAMETER                APPROXIMATE        STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  cof          1.00009e-03   4.94991e-06  -0.00000e+00   0.00000e+00
2  nbkg         1.84966e+02   1.39528e+01  -1.39940e-02  -4.84734e-02
3  nsig         9.99999e+00   2.29848e+00  -1.67401e-04   2.73650e-06
ERR DEF= 0.5
**********
**   95 **HESSE        1500
**********
MNHESS FAILS AND WILL RETURN DIAGONAL MATRIX.
FCN=-1505.32 FROM HESSE     STATUS=FAILED          5 CALLS         113 TOTAL
EDM=1.60915e-05    STRATEGY= 1  ERROR MATRIX UNCERTAINTY 100.0 per cent
EXT PARAMETER                APPROXIMATE     INTERNAL      INTERNAL
NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE
1  cof          7.01340e-03   6.00835e-03  -0.00000e+00  -1.56884e+00
2  nbkg         1.84966e+02   1.39528e+01  -1.39940e-02  -2.63164e-01
3  nsig         9.99999e+00   2.29848e+00  -1.67401e-04   1.56868e+00
ERR DEF= 0.5
EvaluateProfileLikelihood - mu hat = 0.0070134, uncond ML = -1505.32, cond ML = -1505.32 pll = 0 time (create/fit1/2) 0.01 , 0.04 , 0
``````

As to the model, it’s not very “straight forward”, a C++ script describes it.
In the C++ script, I have called another function(defined at the top of this C++ script).
Do you think this is too complex for RooFit to get a correct minimum value ?
Any suggestions to rescue it ?

Thanks !

Also, I post two plots which represent pll ratio and parameter for POI = 0.001.
Are these two plots you asked for ?
Could you please tell me what you can interpret from these plots ?

Best,
Junhui
BackupOOne10GeVPdf.cxx (4.29 KB)

Hi,

I suspect the problem is caused by the correlation of your parameters. To confirm this, it would be better if you run Minuit2, ,which has a much better and clearer output and use a print level >= 3.

Thanks

Lorenzo

Hi, Lorenzo,

I have set the print level to 3 and some of the output are here.

BTW, although the number of signal events is supposed to < 1, and the total number of events in data is 198, according to some one’s suggestion, I have set the model as " Sum(nsig[0,500]* sig_pdf + nbkg[0,10] * bkg_pdf)" to get a conservative limit.

The background model is a linear function, “a” is the intercept, “b” is the slope and has been set as a global constant. “cof” is the POI, proportional to the cross-section.

This box contains only conditional fit.

``````
Do conditional fit
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
**********
**    1 **SET PRINT           1
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 a            1.95490e+00  3.00551e-01    1.36700e+00  1.95500e+00
MINUIT WARNING IN PARAMETR
============== VARIABLE1 BROUGHT BACK INSIDE LIMITS.
2 nbkg         4.88209e+00  3.26092e+00    0.00000e+00  1.00000e+01
3 nsig         1.11119e+02  1.08964e+01    0.00000e+00  5.00000e+02
**********
**    3 **SET ERR         0.5
**********
**********
**    4 **SET PRINT           1
**********
**********
**    5 **SET STR           1
**********
NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
**    6 **MINIMIZE        1500           1
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
FCN=-287.289 FROM MIGRAD    STATUS=INITIATE        8 CALLS           9 TOTAL
EDM= unknown      STRATEGY= 1      NO ERROR MATRIX
EXT PARAMETER               CURRENT GUESS       STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.95490e+00   3.00551e-01   7.95732e-01  -5.37758e-06
2  nbkg         4.88209e+00   3.26092e+00   7.10879e-01   2.36037e-04
3  nsig         1.11119e+02   1.08964e+01   5.24745e-02   9.38450e-04
ERR DEF= 0.5
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-287.289 FROM MIGRAD    STATUS=CONVERGED      35 CALLS          36 TOTAL
EDM=1.24872e-09    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.95500e+00   3.01004e-01   5.00000e-01** at limit **
2  nbkg         4.88152e+00   3.26063e+00   8.15772e-03   1.38313e-05
3  nsig         1.11118e+02   1.08963e+01   6.01986e-04  -6.10947e-04
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  3    ERR DEF=0.5
1.864e-10  4.887e-07 -4.879e-07
4.887e-07  1.262e+01 -7.723e+00
-4.879e-07 -7.723e+00  1.188e+02
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3
1  0.01016   1.000  0.010 -0.003
2  0.19967   0.010  1.000 -0.199
3  0.19945  -0.003 -0.199  1.000
EvaluateProfileLikelihood - mu hat = 0.00218457, uncond ML = -287.289, cond ML = -287.289 pll = -8.59184e-08 time (create/fit1/2) 6.7 , 2.56 , 0.06
POIs:
1) 0x39800f0 RooRealVar:: cof = 0.005  L(0 - 0.02)  "cof"
reusing NLL 0x390af30 new data = 0x7f5956c8b254
Do unconditional fit
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
**********
**    1 **SET PRINT           1
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 a            1.36700e+00  4.27634e-01    1.36700e+00  1.95500e+00
MINUIT WARNING IN PARAMETR
============== VARIABLE1 IS AT ITS LOWER ALLOWED LIMIT.
MINUIT WARNING IN PARAMETR
============== VARIABLE1 BROUGHT BACK INSIDE LIMITS.
2 cof          5.00000e-03  2.00000e-03    0.00000e+00  2.00000e-02
3 nbkg         1.00000e+01  6.49452e-02    0.00000e+00  1.00000e+01
MINUIT WARNING IN PARAM DEF
============== STARTING VALUE IS AT LIMIT.
MINUIT WARNING IN PARAMETR
============== VARIABLE3 IS AT ITS UPPER ALLOWED LIMIT.
MINUIT WARNING IN PARAMETR
============== VARIABLE3 BROUGHT BACK INSIDE LIMITS.
4 nsig         1.12179e+02  1.19052e+01    0.00000e+00  5.00000e+02
**********
**    3 **SET ERR         0.5
**********
**********
**    4 **SET PRINT           1
**********
**********
**    5 **SET STR           1
**********
NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
**    6 **MINIMIZE        2000           1
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
MINUIT WARNING IN MINImize
============== VARIABLE1 IS AT ITS LOWER ALLOWED LIMIT.
MINUIT WARNING IN MINImize
============== VARIABLE3 IS AT ITS UPPER ALLOWED LIMIT.
START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
FCN=-296.112 FROM MIGRAD    STATUS=INITIATE       54 CALLS          55 TOTAL
EDM= unknown      STRATEGY= 1      NO ERROR MATRIX
EXT PARAMETER               CURRENT GUESS       STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.95484e+00   4.27634e-01   0.00000e+00   2.98971e-06
2  cof          1.60770e-02   2.00000e-03   0.00000e+00  -5.68434e-13
3  nbkg         9.82522e+00   6.49452e-02  -2.63231e-01   1.20495e-03
4  nsig         1.12179e+02   1.19052e+01   0.00000e+00   5.56232e+00
ERR DEF= 0.5
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
MINUIT WARNING IN HESSE
============== Negative diagonal element 2 in Error Matrix
MINUIT WARNING IN HESSE
============== 1 added to diagonal of error matrix
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-296.155 FROM MIGRAD    STATUS=CONVERGED     104 CALLS         105 TOTAL
EDM=3.66815e-05    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.95500e+00   1.35141e-01   5.00000e-01  -1.43457e-07
2  cof          1.76543e-02   5.41501e-03   5.00000e-01   1.70530e-12
3  nbkg         9.99823e+00   2.25075e+00   8.23343e-02  -5.24182e-04
4  nsig         1.08901e+02   1.06544e+01   6.15052e-04  -1.16799e-01
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  4    ERR DEF=0.5
2.806e-07  1.550e-18 -3.040e-11 -3.202e-08
1.550e-18  4.141e-05 -1.157e-15 -3.186e-16
-3.040e-11 -1.157e-15  1.733e-02  4.771e-03
-3.202e-08 -3.186e-16  4.771e-03  1.136e+02
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3      4
1  0.00001   1.000  0.000 -0.000 -0.000
2  0.00000   0.000  1.000 -0.000 -0.000
3  0.00340  -0.000 -0.000  1.000  0.003
4  0.00340  -0.000 -0.000  0.003  1.000
EvaluateProfileLikelihood - mu hat = 0.0176543, uncond ML = -296.155, cond ML = -296.155 pll = 0 time (create/fit1/2) 6.89 , 2.58 , 0
POIs:
1) 0x3a32eb0 RooRealVar:: cof = 0.005  L(0 - 0.02)  "cof"
reusing NLL 0x390af30 new data = 0x7f5956c8bf74
Do unconditional fit
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
**********
**    7 **SET PRINT           1
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 a            1.36700e+00  4.27634e-01    1.36700e+00  1.95500e+00
MINUIT WARNING IN PARAMETR
============== VARIABLE1 IS AT ITS LOWER ALLOWED LIMIT.
MINUIT WARNING IN PARAMETR
============== VARIABLE1 BROUGHT BACK INSIDE LIMITS.
2 cof          5.00000e-03  2.00000e-03    0.00000e+00  2.00000e-02
3 nbkg         1.00000e+01  6.49452e-02    0.00000e+00  1.00000e+01
MINUIT WARNING IN PARAM DEF
============== STARTING VALUE IS AT LIMIT.
MINUIT WARNING IN PARAMETR
============== VARIABLE3 IS AT ITS UPPER ALLOWED LIMIT.
MINUIT WARNING IN PARAMETR
============== VARIABLE3 BROUGHT BACK INSIDE LIMITS.
4 nsig         1.12179e+02  1.19052e+01    0.00000e+00  5.00000e+02
**********
**    9 **SET ERR         0.5
**********
**********
**   10 **SET PRINT           1
**********
**********
**   11 **SET STR           1
**********
NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
**   12 **MINIMIZE        2000           1
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
MINUIT WARNING IN MINImize
============== VARIABLE1 IS AT ITS LOWER ALLOWED LIMIT.
MINUIT WARNING IN MINImize
============== VARIABLE3 IS AT ITS UPPER ALLOWED LIMIT.
START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
FCN=-251.959 FROM MIGRAD    STATUS=INITIATE       50 CALLS          51 TOTAL
EDM= unknown      STRATEGY= 1      NO ERROR MATRIX
EXT PARAMETER               CURRENT GUESS       STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.36700e+00   4.27634e-01   0.00000e+00   8.13339e-05
2  cof          4.39747e-03   2.00000e-03   0.00000e+00  -5.68434e-14
3  nbkg         7.74402e+00   6.49452e-02  -9.87910e-01  -6.01744e-02
4  nsig         1.12179e+02   1.19052e+01   0.00000e+00   2.42353e+01
ERR DEF= 0.5
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-252.804 FROM MIGRAD    STATUS=CONVERGED     103 CALLS         104 TOTAL
EDM=1.32709e-05    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.36700e+00   3.29811e-01   6.09211e-02** at limit **
2  cof          1.22672e-02   1.28813e-02   5.00000e-01   9.94760e-13
3  nbkg         8.67851e+00   7.64122e+00   1.22247e-02  -2.98941e-03
4  nsig         9.82959e+01   1.02371e+01   5.59129e-04  -3.63386e-02
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  4    ERR DEF=0.5
2.480e-10  7.851e-09  2.132e-07 -2.138e-07
7.851e-09  2.086e+08  7.530e-01  1.912e+00
2.132e-07  7.530e-01  1.525e+01 -6.575e+00
-2.138e-07  1.912e+00 -6.575e+00  1.049e+02
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3      4
1  0.00355   1.000  0.000  0.003 -0.001
2  0.00002   0.000  1.000  0.000  0.000
3  0.16440   0.003  0.000  1.000 -0.164
4  0.16437  -0.001  0.000 -0.164  1.000
EvaluateProfileLikelihood - mu hat = 0.0122672, uncond ML = -252.804, cond ML = -252.804 pll = 0 time (create/fit1/2) 6.16 , 2.86 , 0
POIs:
1) 0x3a0bd60 RooRealVar:: cof = 0.005  L(0 - 0.02)  "cof"
reusing NLL 0x390af30 new data = 0x7f5956c8cc94
Do unconditional fit
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
**********
**   13 **SET PRINT           1
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 a            1.36700e+00  4.27634e-01    1.36700e+00  1.95500e+00
MINUIT WARNING IN PARAMETR
============== VARIABLE1 IS AT ITS LOWER ALLOWED LIMIT.
MINUIT WARNING IN PARAMETR
============== VARIABLE1 BROUGHT BACK INSIDE LIMITS.
2 cof          5.00000e-03  2.00000e-03    0.00000e+00  2.00000e-02
3 nbkg         1.00000e+01  6.49452e-02    0.00000e+00  1.00000e+01
MINUIT WARNING IN PARAM DEF
============== STARTING VALUE IS AT LIMIT.
MINUIT WARNING IN PARAMETR
============== VARIABLE3 IS AT ITS UPPER ALLOWED LIMIT.
MINUIT WARNING IN PARAMETR
============== VARIABLE3 BROUGHT BACK INSIDE LIMITS.
4 nsig         1.12179e+02  1.19052e+01    0.00000e+00  5.00000e+02
**********
**   15 **SET ERR         0.5
**********
**********
**   16 **SET PRINT           1
**********
**********
**   17 **SET STR           1
**********
NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
**   18 **MINIMIZE        2000           1
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
MINUIT WARNING IN MINImize
============== VARIABLE1 IS AT ITS LOWER ALLOWED LIMIT.
MINUIT WARNING IN MINImize
============== VARIABLE3 IS AT ITS UPPER ALLOWED LIMIT.
START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
FCN=-312.486 FROM MIGRAD    STATUS=INITIATE       77 CALLS          78 TOTAL
EDM= unknown      STRATEGY= 1      NO ERROR MATRIX
EXT PARAMETER               CURRENT GUESS       STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.92648e+00   4.27634e-01   0.00000e+00  -2.77859e-03
2  cof          5.14830e-05   2.00000e-03   0.00000e+00  -4.70711e-02
3  nbkg         5.30516e+00   6.49452e-02  -1.50777e+00   9.05373e-02
4  nsig         1.12179e+02   1.19052e+01   0.00000e+00  -6.71639e+00
ERR DEF= 0.5
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-312.556 FROM HESSE     STATUS=OK             23 CALLS         140 TOTAL
EDM=0.054717    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.95486e+00   5.84822e-01   1.74554e-01   1.30119e-04
2  cof          4.18701e-05   7.00220e-05   5.28366e-02   4.31448e+00
3  nbkg         4.76346e+00   3.35774e+00   9.05320e-03  -8.29083e-04
4  nsig         1.16231e+02   1.11750e+01   6.32297e-04  -8.17952e-03
ERR DEF= 0.5
FCN=-312.556 FROM MIGRAD    STATUS=CONVERGED     156 CALLS         157 TOTAL
EDM=2.20013e-06    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   0.0 per cent
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.95488e+00   5.84926e-01  -3.02160e-03   1.17328e-04
2  cof          4.42900e-05   2.31211e-05  -2.61012e-03   1.61375e-11
3  nbkg         4.76194e+00   3.35739e+00  -3.05587e-04  -1.38771e-03
4  nsig         1.16233e+02   1.11749e+01   9.79798e-06  -6.30687e-03
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  4    ERR DEF=0.5
1.675e-02  1.307e-10 -9.446e-03  9.417e-03
1.307e-10  5.347e-10 -1.165e-08  1.216e-09
-9.446e-03 -1.165e-08  1.356e+01 -8.771e+00
9.417e-03  1.216e-09 -8.771e+00  1.250e+02
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3      4
1  0.01996   1.000  0.000 -0.020  0.007
2  0.00014   0.000  1.000 -0.000  0.000
3  0.21388  -0.020 -0.000  1.000 -0.213
4  0.21309   0.007  0.000 -0.213  1.000
Do conditional fit
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
**********
**    1 **SET PRINT           1
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 a            1.95488e+00  5.84926e-01    1.36700e+00  1.95500e+00
MINUIT WARNING IN PARAMETR
============== VARIABLE1 BROUGHT BACK INSIDE LIMITS.
2 nbkg         4.76194e+00  3.35739e+00    0.00000e+00  1.00000e+01
3 nsig         1.16233e+02  1.11749e+01    0.00000e+00  5.00000e+02
**********
**    3 **SET ERR         0.5
**********
**********
**    4 **SET PRINT           1
**********
**********
**    5 **SET STR           1
**********
NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
**    6 **MINIMIZE        1500           1
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
FCN=-312.546 FROM MIGRAD    STATUS=INITIATE        8 CALLS           9 TOTAL
EDM= unknown      STRATEGY= 1      NO ERROR MATRIX
EXT PARAMETER               CURRENT GUESS       STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.95488e+00   5.84926e-01   1.49886e+00  -1.17410e-04
2  nbkg         4.76194e+00   3.35739e+00   7.38087e-01  -1.63869e-03
3  nsig         1.16233e+02   1.11749e+01   5.29656e-02  -5.84673e-03
ERR DEF= 0.5
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-312.546 FROM MIGRAD    STATUS=CONVERGED      33 CALLS          34 TOTAL
EDM=6.4847e-08    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.95500e+00   5.85325e-01   1.89809e-01** at limit **
2  nbkg         4.76618e+00   3.35809e+00   8.79733e-03   1.01061e-04
3  nsig         1.16237e+02   1.11754e+01   6.31901e-04   4.90955e-03
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  3    ERR DEF=0.5
1.520e-09 -2.276e-06  2.269e-06
-2.276e-06  1.356e+01 -8.774e+00
2.269e-06 -8.774e+00  1.250e+02
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3
1  0.01596   1.000 -0.016  0.005
2  0.21358  -0.016  1.000 -0.213
3  0.21308   0.005 -0.213  1.000
EvaluateProfileLikelihood - mu hat = 4.429e-05, uncond ML = -312.556, cond ML = -312.546 pll = 0.00951574 time (create/fit1/2) 6.96 , 2.06 , 0.06
[#1] INFO:InputArguments -- Profiling conditional MLEs for Alt.
[#1] INFO:InputArguments -- Using a ToyMCSampler. Now configuring for Alt.
POIs:
1) 0x390c650 RooRealVar:: cof = 0.005  L(0 - 0.02)  "cof"
reusing NLL 0x390af30 new data = 0x7f5956c8dc54
Do unconditional fit
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 a            1.95500e+00  1.33098e-01    1.36700e+00  1.95500e+00
2 cof          5.00000e-03  2.00000e-03    0.00000e+00  2.00000e-02
3 nbkg         1.00000e+01  6.14922e+00    0.00000e+00  1.00000e+01
4 nsig         1.89018e+02  1.40750e+01    0.00000e+00  5.00000e+02
**********
**   20 **SET ERR         0.5
**********
**********
**   21 **SET PRINT           1
**********
**********
**   22 **SET STR           1
**********
NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
**   23 **MINIMIZE        2000           1
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
FCN=-97.1113 FROM MIGRAD    STATUS=INITIATE       33 CALLS          34 TOTAL
EDM= unknown      STRATEGY= 1      NO ERROR MATRIX
EXT PARAMETER               CURRENT GUESS       STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.95500e+00   1.33098e-01  -0.00000e+00  -5.04132e-04
2  cof          5.30878e-03   2.00000e-03   3.53029e-02  -2.41525e-13
3  nbkg         9.99999e+00   6.14922e+00  -0.00000e+00  -7.10446e-02
4  nsig         1.89018e+02   1.40750e+01  -0.00000e+00   1.04881e+02
ERR DEF= 0.5
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-123.033 FROM MIGRAD    STATUS=CONVERGED      78 CALLS          79 TOTAL
EDM=3.52221e-08    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.95500e+00   1.05221e-01   1.37715e-02** at limit **
2  cof          5.38427e-03   7.46470e-03   5.00000e-01   1.70530e-12
3  nbkg         1.00000e+01   5.41112e-02   1.14054e-03** at limit **
4  nsig         8.97641e+01   1.09763e+01   4.38415e-04  -8.41518e-04
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  4    ERR DEF=0.5
5.739e-10 -3.065e-18  1.753e-18  2.050e-09
-3.065e-18  7.869e-05 -9.364e-27 -1.095e-17
1.753e-18 -9.364e-27  3.962e-10  2.479e-08
2.050e-09 -1.095e-17  2.479e-08  1.206e+02
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3      4
1  0.00001   1.000 -0.000  0.000  0.000
2  0.00000  -0.000  1.000 -0.000 -0.000
3  0.00011   0.000 -0.000  1.000  0.000
4  0.00011   0.000 -0.000  0.000  1.000
EvaluateProfileLikelihood - mu hat = 0.00538427, uncond ML = -123.033, cond ML = -123.033 pll = 0 time (create/fit1/2) 10.86 , 2.5 , 0
POIs:
1) 0x39ef0f0 RooRealVar:: cof = 0.005  L(0 - 0.02)  "cof"
reusing NLL 0x390af30 new data = 0x7f5956c8ec14
Do unconditional fit
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
**********
**   24 **SET PRINT           1
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 a            1.95500e+00  1.33098e-01    1.36700e+00  1.95500e+00
2 cof          5.00000e-03  2.00000e-03    0.00000e+00  2.00000e-02
3 nbkg         1.00000e+01  6.14922e+00    0.00000e+00  1.00000e+01
4 nsig         1.89018e+02  1.40750e+01    0.00000e+00  5.00000e+02
**********
**   26 **SET ERR         0.5
**********
**********
**   27 **SET PRINT           1
**********
**********
**   28 **SET STR           1
**********
NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
**   29 **MINIMIZE        2000           1
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
FCN=-157.631 FROM MIGRAD    STATUS=INITIATE       28 CALLS          29 TOTAL
EDM= unknown      STRATEGY= 1      NO ERROR MATRIX
EXT PARAMETER               CURRENT GUESS       STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.95500e+00   1.33098e-01   0.00000e+00  -4.73793e-04
2  cof          4.53430e-03   2.00000e-03  -5.46645e-02   4.83049e-13
3  nbkg         9.99999e+00   6.14922e+00   0.00000e+00  -6.51200e-02
4  nsig         1.89018e+02   1.40750e+01   0.00000e+00   8.42725e+01
ERR DEF= 0.5
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-173.342 FROM MIGRAD    STATUS=CONVERGED      71 CALLS          72 TOTAL
EDM=5.30226e-08    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.95500e+00   1.06983e-01   1.69773e-02** at limit **
2  cof          4.65170e-03   7.11009e-03   5.00000e-01   2.84217e-12
3  nbkg         1.00000e+01   6.13587e-02   1.44147e-03** at limit **
4  nsig         1.10677e+02   1.18486e+01   5.17562e-04  -3.34167e-03
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  4    ERR DEF=0.5
2.629e-10  1.617e-18  1.516e-18  1.794e-09
1.617e-18  7.140e-05  9.324e-27  1.104e-17
1.516e-18  9.324e-27  2.597e-10  2.674e-08
1.794e-09  1.104e-17  2.674e-08  1.405e+02
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3      4
1  0.00001   1.000  0.000  0.000  0.000
2  0.00000   0.000  1.000  0.000  0.000
3  0.00014   0.000  0.000  1.000  0.000
4  0.00014   0.000  0.000  0.000  1.000``````

This contains both conditional fit and unconditional fit.

``````
Do conditional fit
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
**********
**    1 **SET PRINT           1
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 a            1.36700e+00  4.49039e-01    1.36700e+00  1.95500e+00
MINUIT WARNING IN PARAMETR
============== VARIABLE1 IS AT ITS LOWER ALLOWED LIMIT.
MINUIT WARNING IN PARAMETR
============== VARIABLE1 BROUGHT BACK INSIDE LIMITS.
2 nbkg         1.00000e+01  5.64637e-02    0.00000e+00  1.00000e+01
MINUIT WARNING IN PARAMETR
============== VARIABLE2 IS AT ITS UPPER ALLOWED LIMIT.
MINUIT WARNING IN PARAMETR
============== VARIABLE2 BROUGHT BACK INSIDE LIMITS.
3 nsig         1.02614e+02  1.15464e+01    0.00000e+00  5.00000e+02
**********
**    3 **SET ERR         0.5
**********
**********
**    4 **SET PRINT           1
**********
**********
**    5 **SET STR           1
**********
NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
**    6 **MINIMIZE        1500           1
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
MINUIT WARNING IN MINImize
============== VARIABLE1 IS AT ITS LOWER ALLOWED LIMIT.
MINUIT WARNING IN MINImize
============== VARIABLE2 IS AT ITS UPPER ALLOWED LIMIT.
START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
FCN=-157.106 FROM MIGRAD    STATUS=INITIATE        8 CALLS           9 TOTAL
EDM= unknown      STRATEGY= 1      NO ERROR MATRIX
EXT PARAMETER               CURRENT GUESS       STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.36700e+00   4.49039e-01   1.06216e+00   7.39176e-04
2  nbkg         9.99999e+00   5.64637e-02   7.42430e-02  -8.63141e-02
3  nsig         1.02614e+02   1.15464e+01   5.72603e-02  -4.51273e-05
ERR DEF= 0.5
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-157.106 FROM MIGRAD    STATUS=CONVERGED      33 CALLS          34 TOTAL
EDM=1.33672e-11    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.36700e+00   4.49039e-01   1.40916e-02** at limit **
2  nbkg         1.00000e+01   5.64637e-02   1.30405e-03** at limit **
3  nsig         1.02614e+02   1.15464e+01   4.95958e-04   6.39056e-05
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  3    ERR DEF=0.5
2.828e-16  6.021e-26  3.063e-12
6.021e-26  1.947e-19  6.674e-13
3.063e-12  6.674e-13  1.335e+02
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3
1  0.00002   1.000  0.000  0.000
2  0.00013   0.000  1.000  0.000
3  0.00013   0.000  0.000  1.000
EvaluateProfileLikelihood - mu hat = 0.00489964, uncond ML = -157.106, cond ML = -157.106 pll = 5.11591e-12 time (create/fit1/2) 11.53 , 4.89 , 0.06
POIs:
1) 0x3abc3c0 RooRealVar:: cof = 0.01  L(0 - 0.02)  "cof"
reusing NLL 0x390af30 new data = 0x7f5956c9a134
Do unconditional fit
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
**********
**    1 **SET PRINT           1
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 a            1.95500e+00  1.33098e-01    1.36700e+00  1.95500e+00
MINUIT WARNING IN PARAMETR
============== VARIABLE1 BROUGHT BACK INSIDE LIMITS.
2 cof          1.00000e-02  2.00000e-03    0.00000e+00  2.00000e-02
3 nbkg         1.00000e+01  6.14922e+00    0.00000e+00  1.00000e+01
MINUIT WARNING IN PARAMETR
============== VARIABLE3 IS AT ITS UPPER ALLOWED LIMIT.
MINUIT WARNING IN PARAMETR
============== VARIABLE3 BROUGHT BACK INSIDE LIMITS.
4 nsig         1.89018e+02  1.40750e+01    0.00000e+00  5.00000e+02
**********
**    3 **SET ERR         0.5
**********
**********
**    4 **SET PRINT           1
**********
**********
**    5 **SET STR           1
**********
NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
**    6 **MINIMIZE        2000           1
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
MINUIT WARNING IN MINImize
============== VARIABLE3 IS AT ITS UPPER ALLOWED LIMIT.
START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
FCN=-205.909 FROM MIGRAD    STATUS=INITIATE       51 CALLS          52 TOTAL
EDM= unknown      STRATEGY= 1      NO ERROR MATRIX
EXT PARAMETER               CURRENT GUESS       STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.36702e+00   1.33098e-01  -0.00000e+00   8.47532e-03
2  cof          1.72113e-02   2.00000e-03   8.05432e-01  -1.13687e-13
3  nbkg         9.99999e+00   6.14922e+00  -0.00000e+00  -6.07579e-02
4  nsig         1.89018e+02   1.40750e+01  -0.00000e+00   7.08471e+01
ERR DEF= 0.5
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
MINUIT WARNING IN HESSE
============== Negative diagonal element 2 in Error Matrix
MINUIT WARNING IN HESSE
============== 1 added to diagonal of error matrix
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-216.562 FROM MIGRAD    STATUS=CONVERGED      94 CALLS          95 TOTAL
EDM=8.38288e-08    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.36700e+00   8.38157e-02   1.24457e-02** at limit **
2  cof          1.71237e-02   5.90547e-03   5.00000e-01  -1.13687e-13
3  nbkg         1.00000e+01   6.74954e-02   1.69192e-03** at limit **
4  nsig         1.24086e+02   1.23452e+01   5.79150e-04  -3.58836e-03
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  4    ERR DEF=0.5
6.460e-09  0.000e+00  6.938e-18  8.005e-09
0.000e+00  4.925e-05  0.000e+00  0.000e+00
6.938e-18  0.000e+00  1.617e-10  2.508e-08
8.005e-09  0.000e+00  2.508e-08  1.526e+02
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3      4
1  0.00001   1.000  0.000  0.000  0.000
2  0.00000   0.000  1.000  0.000  0.000
3  0.00016   0.000  0.000  1.000  0.000
4  0.00016   0.000  0.000  0.000  1.000
EvaluateProfileLikelihood - mu hat = 0.0171237, uncond ML = -216.562, cond ML = -216.562 pll = 0 time (create/fit1/2) 11.73 , 2.6 , 0
[#1] INFO:ObjectHandling -- RooWorkspace::saveSnaphot(w) replacing previous snapshot with name ModelConfig__snapshot

=== Using the following for ModelConfig ===
Observables:             RooArgSet:: = (x)
Parameters of Interest:  RooArgSet:: = (cof)
Nuisance Parameters:     RooArgSet:: = (a,nsig,nbkg)
Global Observables:      RooArgSet:: = (b)
PDF:                     RooAddPdf::model[ nsig * sig_pdf + nbkg * bkg_pdf ] = 233.632
Snapshot:
1) 0x3a1fb60 RooRealVar:: cof = 0.015  L(0 - 0.02)  "cof"

=== Using the following for ModelConfig_with_poi_0 ===
Observables:             RooArgSet:: = (x)
Parameters of Interest:  RooArgSet:: = (cof)
Nuisance Parameters:     RooArgSet:: = (a,nsig,nbkg)
Global Observables:      RooArgSet:: = (b)
PDF:                     RooAddPdf::model[ nsig * sig_pdf + nbkg * bkg_pdf ] = 233.632
Snapshot:
1) 0x3a1fb60 RooRealVar:: cof = 0  L(0 - 0.02)  "cof"

POIs:
1) 0x39d2550 RooRealVar:: cof = 0.015  L(0 - 0.02)  "cof"
reusing NLL 0x390af30 new data = 0x7f5956c7f554
Do unconditional fit
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
**********
**    7 **SET PRINT           1
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 a            1.66100e+00  5.88000e-02    1.36700e+00  1.95500e+00
2 cof          1.50000e-02  2.00000e-03    0.00000e+00  2.00000e-02
3 nbkg         1.00000e+00  5.00000e-01    0.00000e+00  1.00000e+01
4 nsig         1.00000e+00  5.00000e-01    0.00000e+00  5.00000e+02
**********
**    9 **SET ERR         0.5
**********
**********
**   10 **SET PRINT           1
**********
**********
**   11 **SET STR           1
**********
NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
**   12 **MINIMIZE        2000           1
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
FCN=356.256 FROM MIGRAD    STATUS=INITIATE       33 CALLS          34 TOTAL
EDM= unknown      STRATEGY= 1      NO ERROR MATRIX
EXT PARAMETER               CURRENT GUESS       STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.36704e+00   5.88000e-02  -1.55373e+00   5.39469e-03
2  cof          1.50000e-02   2.00000e-03   0.00000e+00   0.00000e+00
3  nbkg         1.00000e+00   5.00000e-01   0.00000e+00  -4.22301e+02
4  nsig         1.00000e+00   5.00000e-01   0.00000e+00  -1.25615e+03
ERR DEF= 0.5
MINUIT WARNING IN HESSE
============== Negative diagonal element 2 in Error Matrix
MINUIT WARNING IN HESSE
============== 1.01875 added to diagonal of error matrix
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-185.498 FROM HESSE     STATUS=OK             25 CALLS         217 TOTAL
EDM=1.09869e-05    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.36700e+00   9.41293e-02   1.39356e-02** at limit **
2  cof          1.50801e-03   4.44358e-03   5.00000e-01   4.68761e-03
3  nbkg         1.00000e+01   6.32707e-02   1.51955e-03** at limit **
4  nsig         1.12179e+02   1.18855e+01   5.37825e-04  -1.49632e-05
ERR DEF= 0.5
FCN=-185.498 FROM MIGRAD    STATUS=CONVERGED     234 CALLS         235 TOTAL
EDM=2.74349e-14    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   0.0 per cent
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.36700e+00   9.41293e-02   1.91346e-07** at limit **
2  cof          1.48335e-03   4.41003e-03  -4.68761e-03  -2.47953e-12
3  nbkg         1.00000e+01   6.32707e-02  -1.39791e-07** at limit **
4  nsig         1.12179e+02   1.18855e+01   4.86321e-08  -2.96596e-06
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  4    ERR DEF=0.5
1.067e-14 -1.854e-14  9.363e-25  1.595e-11
-1.854e-14  2.747e-05  7.595e-17 -2.248e-06
9.363e-25  7.595e-17  8.856e-18  5.330e-12
1.595e-11 -2.248e-06  5.330e-12  1.414e+02
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3      4
1  0.00004   1.000 -0.000  0.000  0.000
2  0.00005  -0.000  1.000  0.000 -0.000
3  0.00015   0.000  0.000  1.000  0.000
4  0.00016   0.000 -0.000  0.000  1.000
Do conditional fit
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
**********
**    1 **SET PRINT           1
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 a            1.36700e+00  9.41293e-02    1.36700e+00  1.95500e+00
MINUIT WARNING IN PARAMETR
============== VARIABLE1 IS AT ITS LOWER ALLOWED LIMIT.
MINUIT WARNING IN PARAMETR
============== VARIABLE1 BROUGHT BACK INSIDE LIMITS.
2 nbkg         1.00000e+01  6.32707e-02    0.00000e+00  1.00000e+01
MINUIT WARNING IN PARAM DEF
============== STARTING VALUE IS AT LIMIT.
MINUIT WARNING IN PARAMETR
============== VARIABLE2 IS AT ITS UPPER ALLOWED LIMIT.
MINUIT WARNING IN PARAMETR
============== VARIABLE2 BROUGHT BACK INSIDE LIMITS.
3 nsig         1.12179e+02  1.18855e+01    0.00000e+00  5.00000e+02
**********
**    3 **SET ERR         0.5
**********
**********
**    4 **SET PRINT           1
**********
**********
**    5 **SET STR           1
**********
NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
**    6 **MINIMIZE        1500           1
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
MINUIT WARNING IN MINImize
============== VARIABLE1 IS AT ITS LOWER ALLOWED LIMIT.
MINUIT WARNING IN MINImize
============== VARIABLE2 IS AT ITS UPPER ALLOWED LIMIT.
START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
FCN=-185.498 FROM MIGRAD    STATUS=INITIATE       10 CALLS          11 TOTAL
EDM= unknown      STRATEGY= 1      NO ERROR MATRIX
EXT PARAMETER               CURRENT GUESS       STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.36700e+00   9.41293e-02   4.10656e-01   8.91949e-04
2  nbkg         9.99999e+00   6.32707e-02   7.86565e-02  -7.50206e-02
3  nsig         1.12179e+02   1.18855e+01   5.70547e-02  -6.24751e-05
ERR DEF= 0.5
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-185.498 FROM MIGRAD    STATUS=CONVERGED      35 CALLS          36 TOTAL
EDM=1.27128e-11    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.36700e+00   4.27634e-01   1.39357e-02** at limit **
2  nbkg         1.00000e+01   6.49452e-02   1.51955e-03** at limit **
3  nsig         1.12179e+02   1.19052e+01   5.37825e-04   6.24292e-05
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  3    ERR DEF=0.5
7.572e-16  1.997e-25  7.659e-12
1.997e-25  1.687e-19  7.478e-13
7.659e-12  7.478e-13  1.419e+02
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3
1  0.00002   1.000  0.000  0.000
2  0.00015   0.000  1.000  0.000
3  0.00015   0.000  0.000  1.000
EvaluateProfileLikelihood - mu hat = 0.00148335, uncond ML = -185.498, cond ML = -185.498 pll = 6.70752e-12 time (create/fit1/2) 11.38 , 7.09 , 0.06
[#0] PROGRESS:Generation -- Test Statistic on data: 6.70752e-12
[#1] INFO:InputArguments -- Profiling conditional MLEs for Null.
[#1] INFO:InputArguments -- Using a ToyMCSampler. Now configuring for Null.
POIs:
1) 0x3a8a9c0 RooRealVar:: cof = 0.015  L(0 - 0.02)  "cof"
reusing NLL 0x390af30 new data = 0x7f5956c9b0f4
Do unconditional fit
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 a            1.36700e+00  4.27634e-01    1.36700e+00  1.95500e+00
2 cof          1.50000e-02  2.00000e-03    0.00000e+00  2.00000e-02
3 nbkg         1.00000e+01  6.49452e-02    0.00000e+00  1.00000e+01
4 nsig         1.12179e+02  1.19052e+01    0.00000e+00  5.00000e+02
**********
**   20 **SET ERR         0.5
**********
**********
**   21 **SET PRINT           1
**********
**********
**   22 **SET STR           1
**********
NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
**   23 **MINIMIZE        2000           1
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
FCN=-263.995 FROM MIGRAD    STATUS=INITIATE       32 CALLS          33 TOTAL
EDM= unknown      STRATEGY= 1      NO ERROR MATRIX
EXT PARAMETER               CURRENT GUESS       STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.36700e+00   4.27634e-01   0.00000e+00   2.43997e-05
2  cof          1.50000e-02   2.00000e-03   0.00000e+00   2.15070e-13
3  nbkg         9.12637e+00   6.49452e-02  -5.98157e-01   1.74490e-04
4  nsig         1.12179e+02   1.19052e+01   0.00000e+00   1.35808e+01
ERR DEF= 0.5
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-264.276 FROM MIGRAD    STATUS=CONVERGED      98 CALLS          99 TOTAL
EDM=9.73632e-06    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            1.36700e+00   4.15008e-01   8.64277e-02** at limit **
2  cof          1.39598e-02   1.16289e-02   5.00000e-01  -5.68434e-14
3  nbkg         9.99961e+00   8.97758e+00   4.65633e-02  -7.47456e-04
4  nsig         1.03874e+02   1.05051e+01   5.82517e-04  -1.27706e-02
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  4    ERR DEF=0.5
8.085e-08  6.358e-09  1.611e-08  2.897e-06
6.358e-09  9.271e+07  2.548e-02  1.443e-02
1.611e-08  2.548e-02  6.457e-02  3.657e-02
2.897e-06  1.443e-02  3.657e-02  1.105e+02
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3      4
1  0.00099   1.000  0.000  0.000  0.001
2  0.00001   0.000  1.000  0.000  0.000
3  0.01370   0.000  0.000  1.000  0.014
4  0.01373   0.001  0.000  0.014  1.000``````

How to interpret these information ?

Thanks !

To avoid any possible confusion, I’d like to attach the limit and test statistics corresponding to above messages.
(Because the model is slightly different from my previous posts in this thread, but the symptom is exactly same)

Best,
Junhui

Hi,

For me the fit seems fine, although it is difficult to tell. I notices that you are starting with the parameter “a” at the limit and you get always the limit value. Is this expected ? If this is the case, maybe better to fix that parameter.
I suspect some issue in the model definition. Have you tries to run the Asymptotic calculator. I think it would be easier for me if you can post your workspace which includes not only th model but also the data set you are using and the ModelConfig

Best

Lorenzo