Unstable results when bin contents grow large #2131
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danielwhiteson
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@danielwhiteson before looking at this later today quick note/follow up question: The use of Do you need to use No rush on this as my hunch is that this is caused by model bound constraints so the version used won't matter greatly between |
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Hi, taking one workspace spec resulting in import pyhf
spec = {
"channels": [
{
"name": "singlechannel",
"samples": [
{
"name": "signal",
"data": [
430.0, 1720.0, 14190.0, 43000.0, 81055.0, 61060.0, 19565.0, 10105.0, 6020.0, 4300.0,
3010.0, 2795.0, 2580.0, 430.0, 645.0, 2365.0, 1075.0, 860.0, 215.0, 1075.0, 430.0,
215.0, 215.0, 215.0, 215.0, 0.0, 0.0, 215.0, 0.0, 215.0, 215.0, 0.0, 1505.0,
],
"modifiers": [{"name": "mu", "type": "normfactor", "data": None}],
},
{
"name": "background",
"data": [
111967.78125, 287229.0, 426148.21875, 357975.3125, 348213.125, 292966.90625, 231779.84375, 170498.734375, 115474.328125, 91018.8046875, 80229.0,
60104.76953125, 38717.50390625, 47734.98046875, 28446.408203125, 29647.259765625, 11884.81640625, 17935.529296875, 8182.43994140625, 15784.50390625, 1755.2020263671875, 2653.736083984375,
6868.40185546875, 4312.4521484375, 2058.93994140625, 5768.15869140625, 1229.511962890625, 303.7380065917969, 4312.4521484375, 1008.8599853515625, 2777.90185546875, 1534.550048828125, 13498.7705078125,
], # turn 2058.93994140625 into 2058.9399 and things work
"modifiers": [
{
"name": "uncorr_bkguncrt",
"type": "shapesys",
"data": [
55983.890625,143614.5, 213074.109375, 178987.65625, 174106.5625, 146483.453125, 115889.921875, 85249.3671875, 57737.1640625, 45509.40234375,
40114.5, 30052.384765625, 19358.751953125, 23867.490234375, 14223.2041015625, 14823.6298828125, 5942.408203125, 8967.7646484375, 4091.219970703125, 7892.251953125, 877.6010131835938,
1326.8680419921875, 3434.200927734375, 2156.22607421875, 1029.469970703125, 2884.079345703125, 614.7559814453125, 151.86900329589844, 2156.22607421875, 504.42999267578125, 1388.950927734375, 767.2750244140625, 6749.38525390625,
],
}
],
},
],
}
],
"version": "1.0.0",
"measurements": [
{
"name": "measurement",
"config": {
"poi": "mu",
"parameters": [],
},
}
],
"observations": [
{
"name": "singlechannel",
"data": [
111967, 287229, 426148, 357975, 348213, 292966, 231779, 170498, 115474, 91018, 80229, 60104,
38717, 47734, 28446, 29647, 11884, 17935, 8182, 15784, 1755, 2653, 6868,
4312, 2058, 5768, 1229, 303, 4312, 1008, 2777, 1534, 13498,
],
}
],
}
ws = pyhf.Workspace(spec)
model = ws.model()
data = ws.data(model)
# pyhf.set_backend("numpy", "minuit")
CLs_obs = pyhf.infer.hypotest(1.0, data, model)
print(CLs_obs)I did not spot anything that is obviously wrong here from a quick look. What is probably worth pointing out is that the nuisance parameters in this example get constrained be a very large amount. Looking at the first bin for example, this is a 50% uncertainty in a bin for which your statistical uncertainty is ~0.3%, so that parameter can be constrained by data to an extreme degree. There is no clear conceptual problem that I can see which would impact the minimizer, but it is very unusual and I wonder if that would necessitate some type of step size adjustments. The minimization failure disappears when changing Switching to Minuit for minimization (via the commented out line) fixes this setup for me but causes problems with some others in the original example still. Some of the issues here certainly come from the parameter bounds. A maximum likelihood estimate (with bounds = pdf.config.suggested_bounds()
bounds[0] = (-10, 10)
pyhf.infer.hypotest(..., par_bounds=bounds)which relies on the fact that |
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Hi
The intention was to have a 50% overall *correlated* uncertainty across bins.
I likely misunderstood how to use this workspace builder. What is the correct syntax?
Daniel
… On Mar 10, 2023, at 2:44 PM, Alexander Held ***@***.***> wrote:
Hi, taking one workspace spec resulting in NaN out of the above example (for easier debugging):
import pyhf
spec = {
"channels": [
{
"name": "singlechannel",
"samples": [
{
"name": "signal",
"data": [
430.0, 1720.0, 14190.0, 43000.0, 81055.0, 61060.0, 19565.0, 10105.0, 6020.0, 4300.0,
3010.0, 2795.0, 2580.0, 430.0, 645.0, 2365.0, 1075.0, 860.0, 215.0, 1075.0, 430.0,
215.0, 215.0, 215.0, 215.0, 0.0, 0.0, 215.0, 0.0, 215.0, 215.0, 0.0, 1505.0,
],
"modifiers": [{"name": "mu", "type": "normfactor", "data": None}],
},
{
"name": "background",
"data": [
111967.78125, 287229.0, 426148.21875, 357975.3125, 348213.125, 292966.90625, 231779.84375, 170498.734375, 115474.328125, 91018.8046875, 80229.0,
60104.76953125, 38717.50390625, 47734.98046875, 28446.408203125, 29647.259765625, 11884.81640625, 17935.529296875, 8182.43994140625, 15784.50390625, 1755.2020263671875, 2653.736083984375,
6868.40185546875, 4312.4521484375, 2058.93994140625, 5768.15869140625, 1229.511962890625, 303.7380065917969, 4312.4521484375, 1008.8599853515625, 2777.90185546875, 1534.550048828125, 13498.7705078125,
], # turn 2058.93994140625 into 2058.9399 and things work
"modifiers": [
{
"name": "uncorr_bkguncrt",
"type": "shapesys",
"data": [
55983.890625,143614.5, 213074.109375, 178987.65625, 174106.5625, 146483.453125, 115889.921875, 85249.3671875, 57737.1640625, 45509.40234375,
40114.5, 30052.384765625, 19358.751953125, 23867.490234375, 14223.2041015625, 14823.6298828125, 5942.408203125, 8967.7646484375, 4091.219970703125, 7892.251953125, 877.6010131835938,
1326.8680419921875, 3434.200927734375, 2156.22607421875, 1029.469970703125, 2884.079345703125, 614.7559814453125, 151.86900329589844, 2156.22607421875, 504.42999267578125, 1388.950927734375, 767.2750244140625, 6749.38525390625,
],
}
],
},
],
}
],
"version": "1.0.0",
"measurements": [
{
"name": "measurement",
"config": {
"poi": "mu",
"parameters": [],
},
}
],
"observations": [
{
"name": "singlechannel",
"data": [
111967, 287229, 426148, 357975, 348213, 292966, 231779, 170498, 115474, 91018, 80229, 60104,
38717, 47734, 28446, 29647, 11884, 17935, 8182, 15784, 1755, 2653, 6868,
4312, 2058, 5768, 1229, 303, 4312, 1008, 2777, 1534, 13498,
],
}
],
}
ws = pyhf.Workspace(spec)
model = ws.model()
data = ws.data(model)
# pyhf.set_backend("numpy", "minuit")
CLs_obs = pyhf.infer.hypotest(1.0, data, model)
print(CLs_obs)
I did not spot anything that is obviously wrong here from a quick look. What is probably worth pointing out is that the nuisance parameters in this example get constrained be a very large amount. Looking at the first bin for example, this is a 50% uncertainty in a bin for which your statistical uncertainty is ~0.3%, so that parameter can be constrained by data to an extreme degree. There is no clear conceptual problem that I can see which would impact the minimizer, but it is very unusual and I wonder if that would necessitate some type of step size adjustments.
The minimization failure disappears when changing 2058.93994140625 to 2058.9399 for me which is rather odd. As this is so extremely specific, that may also be machine-dependent.
Switching to Minuit for minimization (via the commented out line) fixes this setup for me but causes problems with some others in the original example still.
Some of the issues here certainly come from the parameter bounds. A maximum likelihood estimate (with mu floating) of the model above will hit the lower bound of mu (withe default range [0, 10]) and that can cause issues for the minimization. You can relax the bounds like this
bounds = pdf.config.suggested_bounds()
bounds[0] = (-10, 10)
pyhf.infer.hypotest(..., par_bounds=bounds)
which relies on the fact that mu is the first parameter of the model (the order is determined by model.config.par_names).
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Thank you!
Unfortunately I don’t seem to have that available.
```console
(pyhf_env) -bash-4.2$ python3
Python 3.6.8 (default, Nov 16 2020, 16:55:22)
[GCC 4.8.5 20150623 (Red Hat 4.8.5-44)] on linux
Type "help", "copyright", "credits" or "license" for more information.
>> import pyhf
>> pyhf.set_backend("numpy")
>> model = pyhf.simplemodels.correlated_background(
... signal=[12.0, 11.0],
... bkg=[50.0, 52.0],
... bkg_up=[45.0, 57.0],
... bkg_down=[55.0, 47.0],
... )
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
AttributeError: module 'pyhf.simplemodels' has no attribute ‘correlated_background'
```
And pip doesn’t want to install 0.7.0 for me:
```console
(pyhf_env) -bash-4.2$ pip install pyhf==0.7.0
ERROR: Could not find a version that satisfies the requirement pyhf==0.7.0 (from versions: 0.0.1, 0.0.3, 0.0.4, 0.0.5, 0.0.8, 0.0.12, 0.0.13, 0.0.14, 0.0.15, 0.0.16, 0.0.17, 0.1.0, 0.1.1, 0.1.2, 0.2.0, 0.2.1, 0.2.2, 0.3.0, 0.3.1, 0.3.2, 0.3.3, 0.3.4, 0.4.0, 0.4.1, 0.4.2, 0.4.3, 0.4.4, 0.5.0, 0.5.1, 0.5.2, 0.5.3, 0.5.4)
ERROR: No matching distribution found for pyhf==0.7.0
```
Any tips?
Daniel
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@danielwhiteson Ah, you're using a very old and now EOL Python which we haven't supported since $ python -m pip install --upgrade norwegianblue
$ eol python
┌───────┬────────────┬─────────┬────────────────┬────────────┐
│ cycle │ release │ latest │ latest release │ eol │
├───────┼────────────┼─────────┼────────────────┼────────────┤
│ 3.11 │ 2022-10-24 │ 3.11.2 │ 2023-02-07 │ 2027-10-24 │
│ 3.10 │ 2021-10-04 │ 3.10.10 │ 2023-02-07 │ 2026-10-04 │
│ 3.9 │ 2020-10-05 │ 3.9.16 │ 2022-12-06 │ 2025-10-05 │
│ 3.8 │ 2019-10-14 │ 3.8.16 │ 2022-12-06 │ 2024-10-14 │
│ 3.7 │ 2018-06-26 │ 3.7.16 │ 2022-12-06 │ 2023-06-27 │
│ 3.6 │ 2016-12-22 │ 3.6.15 │ 2021-09-03 │ 2021-12-23 │
│ 3.5 │ 2015-09-12 │ 3.5.10 │ 2020-09-05 │ 2020-09-13 │
│ 3.4 │ 2014-03-15 │ 3.4.10 │ 2019-03-18 │ 2019-03-18 │
│ 3.3 │ 2012-09-29 │ 3.3.7 │ 2017-09-19 │ 2017-09-29 │
│ 2.7 │ 2010-07-03 │ 2.7.18 │ 2020-04-19 │ 2020-01-01 │
│ 2.6 │ 2008-10-01 │ 2.6.9 │ 2013-10-29 │ 2013-10-29 │
└───────┴────────────┴─────────┴────────────────┴────────────As for what to do in your particular case, here's a few ideas / questions:
$ python3
Python 3.6.8 (default, Nov 16 2020, 16:55:22)
[GCC 4.8.5 20150623 (Red Hat 4.8.5-44)] on linuxI assume that you're on a lab machine (e.g. a group's cluster or deep learning rig)? If so, then I think it should be pretty straightforward to update your CPython version that you're using (or just install a new Python runtime) — hopefully this isn't laughably naive optimism on my part. I could probably give recommendations on this if that would be useful (though that's a bit out of scope for
$ docker pull pyhf/pyhf:v0.7.0
$ docker run --rm -ti --user 1000:1000 -v $PWD:/example -w /example --entrypoint /bin/bash pyhf/pyhf:v0.7.0
I have no name!@541a5388522c:/example$ pyhf --version
pyhf, version 0.7.0
I have no name!@541a5388522c:/example$ |
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Hi!
Thank you. We have python 3.10.7, so I was able to install phyf 0.7.0 in a new environment. I can run with the correlated_background, as you suggest, but the results I’m getting still look odd. Am I using it incorrectly, or is this a symptom of the same underlying problem that plagued my initial results (where I was incorrectly using an uncorrelated bg)?
New log and script below.
Daniel
import pyhf
from scipy.signal import savgol_filter
import numpy as np
pyhf.set_backend("numpy")
#new signals generated from 100,000 events generated for each mass
hist300 = [2.0, 8.0, 66.0, 200.0, 377.0, 284.0, 91.0, 47.0, 28.0, 20.0, 14.0, 13.0, 12.0, 2.0, 3.0, 11.0, 5.0, 4.0, 1.0, 5.0, 2.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0,
0.0, 7.0]
background = [111967.78125, 287229.0, 426148.21875, 357975.3125, 348213.125, 292966.90625, 231779.84375, 170498.734375, 115474.328125, 91018.8046875, 80229.0, 60104.76953125, 38717
.50390625, 47734.98046875, 28446.408203125, 29647.259765625, 11884.81640625, 17935.529296875, 8182.43994140625, 15784.50390625, 1755.2020263671875, 2653.736083984375, 6868.40185546
875, 4312.4521484375, 2058.93994140625, 5768.15869140625, 1229.511962890625, 303.7380065917969, 4312.4521484375, 1008.8599853515625, 2777.90185546875, 1534.550048828125, 13498.7705
078125]
N_events = 100000.0 # number generated
lumin = 100.0 # inverse fb
def findCLs(cs):
hist = hist300
print("Length = ",len(hist))
# statistical evaluation for an example problem in multiple bins
# histograms below should be luminosity scaled, so that the sum over their bins is the total number of expected events
# background histogram, as a list
bkg_hist = background
# background uncertainty, per bin
bkg_uncert_hist_down = [0.5*e for e in bkg_hist]
bkg_uncert_hist_up = [1.5*e for e in bkg_hist]
# signal histogram
signal_hist = [(e*cs*lumin/N_events) for e in hist] #normalizes the signal histogram
# observed data
data_hist = [int(e) for e in bkg_hist]
print ("\n\n========================================================================")
print (" xs = ",cs)
print ("Signal = ",signal_hist)
print ("Bg = ", bkg_hist)
print ("Bg unc + = ", bkg_uncert_hist_up)
print ("Bg unc - = ", bkg_uncert_hist_down)
# make the PDF
pdf = pyhf.simplemodels.correlated_background(
signal=signal_hist,
bkg=bkg_hist,
bkg_up=bkg_uncert_hist_down,
bkg_down=bkg_uncert_hist_up)
# get the results
CLs_obs, CLs_exp = pyhf.infer.hypotest(1.0, data_hist + pdf.config.auxdata, pdf, return_expected=True)
# display
print('Observed: {}, Expected: {}'.format(CLs_obs, CLs_exp))
# Roughly, the expected limit on this hypothesis is at a CL of 1-CLs_exp
# if you want a confidence level of 95%, scale your signal up or down until CLs_exp = 0.05
for i in range(0,30):
cs = 180000.0 + 5000.0*float(i) #the cross section to calculate the CLs value for
findCLs(cs) #change the index parameter (currently 0) to change which signal mass you want to analyze
print(cs)
print()
On Mar 11, 2023, at 2:52 PM, Matthew Feickert ***@***.***> wrote:
@danielwhiteson <https://urldefense.com/v3/__https://github.com/danielwhiteson__;!!CzAuKJ42GuquVTTmVmPViYEvSg!OEDp7rbpoKR6-pF91oQEEEbFHqKQkBL-mao_Qc-lZRNV1EV5rd6whOvvpNtMF-OO6Ih1oyM57wfFZiMS1OH5_g$> Ah, you're using a very old and now EOL Python which we haven't supported since v0.6.0 (v0.6.0 is Python 3.7+, and the next pyhf release will be Python 3.8+). We loosely follow NEP 29 <https://urldefense.com/v3/__https://numpy.org/neps/nep-0029-deprecation_policy.html__;!!CzAuKJ42GuquVTTmVmPViYEvSg!OEDp7rbpoKR6-pF91oQEEEbFHqKQkBL-mao_Qc-lZRNV1EV5rd6whOvvpNtMF-OO6Ih1oyM57wfFZiODTai_uw$> and SPEC 0 <https://urldefense.com/v3/__https://scientific-python.org/specs/spec-0000/__;!!CzAuKJ42GuquVTTmVmPViYEvSg!OEDp7rbpoKR6-pF91oQEEEbFHqKQkBL-mao_Qc-lZRNV1EV5rd6whOvvpNtMF-OO6Ih1oyM57wfFZiNDRTCUQA$> but lag behind by about a year to try to give analysis teams using pyhf enough time to move to modern CPythons. We also announce plans to drop CPython versions on the pyhf-announcements mailing list <https://urldefense.com/v3/__https://groups.google.com/group/pyhf-announcements/subscribe__;!!CzAuKJ42GuquVTTmVmPViYEvSg!OEDp7rbpoKR6-pF91oQEEEbFHqKQkBL-mao_Qc-lZRNV1EV5rd6whOvvpNtMF-OO6Ih1oyM57wfFZiNO9W8EHg$> in the event that any users really need us to support something for longer.
$ python -m pip install --upgrade norwegianblue
$ eol python
┌───────┬────────────┬─────────┬────────────────┬────────────┐
│ cycle │ release │ latest │ latest release │ eol │
├───────┼────────────┼─────────┼────────────────┼────────────┤
│ 3.11 │ 2022-10-24 │ 3.11.2 │ 2023-02-07 │ 2027-10-24 │
│ 3.10 │ 2021-10-04 │ 3.10.10 │ 2023-02-07 │ 2026-10-04 │
│ 3.9 │ 2020-10-05 │ 3.9.16 │ 2022-12-06 │ 2025-10-05 │
│ 3.8 │ 2019-10-14 │ 3.8.16 │ 2022-12-06 │ 2024-10-14 │
│ 3.7 │ 2018-06-26 │ 3.7.16 │ 2022-12-06 │ 2023-06-27 │
│ 3.6 │ 2016-12-22 │ 3.6.15 │ 2021-09-03 │ 2021-12-23 │
│ 3.5 │ 2015-09-12 │ 3.5.10 │ 2020-09-05 │ 2020-09-13 │
│ 3.4 │ 2014-03-15 │ 3.4.10 │ 2019-03-18 │ 2019-03-18 │
│ 3.3 │ 2012-09-29 │ 3.3.7 │ 2017-09-19 │ 2017-09-29 │
│ 2.7 │ 2010-07-03 │ 2.7.18 │ 2020-04-19 │ 2020-01-01 │
│ 2.6 │ 2008-10-01 │ 2.6.9 │ 2013-10-29 │ 2013-10-29 │
└───────┴────────────┴─────────┴────────────────┴────────────
As for what to do in your particular case, here's a few ideas / questions:
Is this the only Python 3 runtime on the machine? If not, is there a more modern CPython version available?
Given that the version of gcc used to compile your CPython is
$ python3
Python 3.6.8 (default, Nov 16 2020, 16:55:22)
[GCC 4.8.5 20150623 (Red Hat 4.8.5-44)] on linux
I assume that you're on a lab machine (e.g. a group's cluster or deep learning rig)? If so, then I think it should be pretty straightforward to update your CPython version that you're using (or just install a new Python runtime) — hopefully this isn't laughably naive optimism on my part. I could probably give recommendations on this if that would be useful (though that's a bit out of scope for pyhf discussions so we should do Python installation questions via email, messages, or call 👍).
Is your student similarly constrained? Or are they working elsewhere and able to use modern releases of pyhf?
Is using a Linux container runtime (e.g. Docker, Apptainer) a possibility? If so, then you could use the images we distribute on Docker Hub <x-msg://29/naive> (pyhf/pyhf:v0.7.0). At the moment though until we take care of Issue #2133 <https://urldefense.com/v3/__https://github.com/scikit-hep/pyhf/issues/2133__;!!CzAuKJ42GuquVTTmVmPViYEvSg!OEDp7rbpoKR6-pF91oQEEEbFHqKQkBL-mao_Qc-lZRNV1EV5rd6whOvvpNtMF-OO6Ih1oyM57wfFZiPUeWFyEg$> you need to throw in some extra runtime flags to have things be in a nice non-root user state.
$ docker pull pyhf/pyhf:v0.7.0
$ docker run --rm -ti --user 1000:1000 -v $PWD:/example -w /example --entrypoint /bin/bash pyhf/pyhf:v0.7.0
I have no ***@***.***:/example$ pyhf --version
pyhf, version 0.7.0
I have no ***@***.***:/example$
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/export/nfs0home/whiteson/.local/lib/python3.10/site-packages/pyhf/infer/calculators.py:467: RuntimeWarning: invalid value encountered in divide
CLs = tensorlib.astensor(CLsb / CLb)
/export/nfs0home/whiteson/.local/lib/python3.10/site-packages/pyhf/infer/calculators.py:418: RuntimeWarning: divide by zero encountered in double_scalars
teststat = (qmu - qmu_A) / (2 * self.sqrtqmuA_v)
Length = 33
========================================================================
xs = 180000.0
Signal = [360.0, 1440.0, 11880.0, 36000.0, 67860.0, 51120.0, 16380.0, 8460.0, 5040.0, 3600.0, 2520.0, 2340.0, 2160.0, 360.0, 540.0, 1980.0, 900.0, 720.0, 180.0, 900.0, 360.0, 180.0, 180.0, 180.0, 180.0, 0.0, 0.0, 180.0, 0.0, 180.0, 180.0, 0.0, 1260.0]
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Observed: 0.0, Expected: 0.0
180000.0
Length = 33
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xs = 185000.0
Signal = [370.0, 1480.0, 12210.0, 37000.0, 69745.0, 52540.0, 16835.0, 8695.0, 5180.0, 3700.0, 2590.0, 2405.0, 2220.0, 370.0, 555.0, 2035.0, 925.0, 740.0, 185.0, 925.0, 370.0, 185.0, 185.0, 185.0, 185.0, 0.0, 0.0, 185.0, 0.0, 185.0, 185.0, 0.0, 1295.0]
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Observed: 0.0, Expected: 0.0
185000.0
Length = 33
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xs = 190000.0
Signal = [380.0, 1520.0, 12540.0, 38000.0, 71630.0, 53960.0, 17290.0, 8930.0, 5320.0, 3800.0, 2660.0, 2470.0, 2280.0, 380.0, 570.0, 2090.0, 950.0, 760.0, 190.0, 950.0, 380.0, 190.0, 190.0, 190.0, 190.0, 0.0, 0.0, 190.0, 0.0, 190.0, 190.0, 0.0, 1330.0]
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Bg unc + = [167951.671875, 430843.5, 639222.328125, 536962.96875, 522319.6875, 439450.359375, 347669.765625, 255748.1015625, 173211.4921875, 136528.20703125, 120343.5, 90157.154296875, 58076.255859375, 71602.470703125, 42669.6123046875, 44470.8896484375, 17827.224609375, 26903.2939453125, 12273.659912109375, 23676.755859375, 2632.8030395507812, 3980.6041259765625, 10302.602783203125, 6468.67822265625, 3088.409912109375, 8652.238037109375, 1844.2679443359375, 455.6070098876953, 6468.67822265625, 1513.2899780273438, 4166.852783203125, 2301.8250732421875, 20248.15576171875]
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Observed: 0.0, Expected: 0.0
190000.0
Length = 33
========================================================================
xs = 195000.0
Signal = [390.0, 1560.0, 12870.0, 39000.0, 73515.0, 55380.0, 17745.0, 9165.0, 5460.0, 3900.0, 2730.0, 2535.0, 2340.0, 390.0, 585.0, 2145.0, 975.0, 780.0, 195.0, 975.0, 390.0, 195.0, 195.0, 195.0, 195.0, 0.0, 0.0, 195.0, 0.0, 195.0, 195.0, 0.0, 1365.0]
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Observed: 0.0, Expected: 0.0
195000.0
Length = 33
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xs = 200000.0
Signal = [400.0, 1600.0, 13200.0, 40000.0, 75400.0, 56800.0, 18200.0, 9400.0, 5600.0, 4000.0, 2800.0, 2600.0, 2400.0, 400.0, 600.0, 2200.0, 1000.0, 800.0, 200.0, 1000.0, 400.0, 200.0, 200.0, 200.0, 200.0, 0.0, 0.0, 200.0, 0.0, 200.0, 200.0, 0.0, 1400.0]
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Bg unc + = [167951.671875, 430843.5, 639222.328125, 536962.96875, 522319.6875, 439450.359375, 347669.765625, 255748.1015625, 173211.4921875, 136528.20703125, 120343.5, 90157.154296875, 58076.255859375, 71602.470703125, 42669.6123046875, 44470.8896484375, 17827.224609375, 26903.2939453125, 12273.659912109375, 23676.755859375, 2632.8030395507812, 3980.6041259765625, 10302.602783203125, 6468.67822265625, 3088.409912109375, 8652.238037109375, 1844.2679443359375, 455.6070098876953, 6468.67822265625, 1513.2899780273438, 4166.852783203125, 2301.8250732421875, 20248.15576171875]
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Observed: 0.0, Expected: 0.0
200000.0
Length = 33
========================================================================
xs = 205000.0
Signal = [410.0, 1640.0, 13530.0, 41000.0, 77285.0, 58220.0, 18655.0, 9635.0, 5740.0, 4100.0, 2870.0, 2665.0, 2460.0, 410.0, 615.0, 2255.0, 1025.0, 820.0, 205.0, 1025.0, 410.0, 205.0, 205.0, 205.0, 205.0, 0.0, 0.0, 205.0, 0.0, 205.0, 205.0, 0.0, 1435.0]
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Bg unc + = [167951.671875, 430843.5, 639222.328125, 536962.96875, 522319.6875, 439450.359375, 347669.765625, 255748.1015625, 173211.4921875, 136528.20703125, 120343.5, 90157.154296875, 58076.255859375, 71602.470703125, 42669.6123046875, 44470.8896484375, 17827.224609375, 26903.2939453125, 12273.659912109375, 23676.755859375, 2632.8030395507812, 3980.6041259765625, 10302.602783203125, 6468.67822265625, 3088.409912109375, 8652.238037109375, 1844.2679443359375, 455.6070098876953, 6468.67822265625, 1513.2899780273438, 4166.852783203125, 2301.8250732421875, 20248.15576171875]
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Observed: 0.0, Expected: 0.0
205000.0
Length = 33
========================================================================
xs = 210000.0
Signal = [420.0, 1680.0, 13860.0, 42000.0, 79170.0, 59640.0, 19110.0, 9870.0, 5880.0, 4200.0, 2940.0, 2730.0, 2520.0, 420.0, 630.0, 2310.0, 1050.0, 840.0, 210.0, 1050.0, 420.0, 210.0, 210.0, 210.0, 210.0, 0.0, 0.0, 210.0, 0.0, 210.0, 210.0, 0.0, 1470.0]
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Bg unc + = [167951.671875, 430843.5, 639222.328125, 536962.96875, 522319.6875, 439450.359375, 347669.765625, 255748.1015625, 173211.4921875, 136528.20703125, 120343.5, 90157.154296875, 58076.255859375, 71602.470703125, 42669.6123046875, 44470.8896484375, 17827.224609375, 26903.2939453125, 12273.659912109375, 23676.755859375, 2632.8030395507812, 3980.6041259765625, 10302.602783203125, 6468.67822265625, 3088.409912109375, 8652.238037109375, 1844.2679443359375, 455.6070098876953, 6468.67822265625, 1513.2899780273438, 4166.852783203125, 2301.8250732421875, 20248.15576171875]
Bg unc - = [55983.890625, 143614.5, 213074.109375, 178987.65625, 174106.5625, 146483.453125, 115889.921875, 85249.3671875, 57737.1640625, 45509.40234375, 40114.5, 30052.384765625, 19358.751953125, 23867.490234375, 14223.2041015625, 14823.6298828125, 5942.408203125, 8967.7646484375, 4091.219970703125, 7892.251953125, 877.6010131835938, 1326.8680419921875, 3434.200927734375, 2156.22607421875, 1029.469970703125, 2884.079345703125, 614.7559814453125, 151.86900329589844, 2156.22607421875, 504.42999267578125, 1388.950927734375, 767.2750244140625, 6749.38525390625]
Observed: 0.0, Expected: 0.0
210000.0
Length = 33
========================================================================
xs = 215000.0
Signal = [430.0, 1720.0, 14190.0, 43000.0, 81055.0, 61060.0, 19565.0, 10105.0, 6020.0, 4300.0, 3010.0, 2795.0, 2580.0, 430.0, 645.0, 2365.0, 1075.0, 860.0, 215.0, 1075.0, 430.0, 215.0, 215.0, 215.0, 215.0, 0.0, 0.0, 215.0, 0.0, 215.0, 215.0, 0.0, 1505.0]
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Bg unc + = [167951.671875, 430843.5, 639222.328125, 536962.96875, 522319.6875, 439450.359375, 347669.765625, 255748.1015625, 173211.4921875, 136528.20703125, 120343.5, 90157.154296875, 58076.255859375, 71602.470703125, 42669.6123046875, 44470.8896484375, 17827.224609375, 26903.2939453125, 12273.659912109375, 23676.755859375, 2632.8030395507812, 3980.6041259765625, 10302.602783203125, 6468.67822265625, 3088.409912109375, 8652.238037109375, 1844.2679443359375, 455.6070098876953, 6468.67822265625, 1513.2899780273438, 4166.852783203125, 2301.8250732421875, 20248.15576171875]
Bg unc - = [55983.890625, 143614.5, 213074.109375, 178987.65625, 174106.5625, 146483.453125, 115889.921875, 85249.3671875, 57737.1640625, 45509.40234375, 40114.5, 30052.384765625, 19358.751953125, 23867.490234375, 14223.2041015625, 14823.6298828125, 5942.408203125, 8967.7646484375, 4091.219970703125, 7892.251953125, 877.6010131835938, 1326.8680419921875, 3434.200927734375, 2156.22607421875, 1029.469970703125, 2884.079345703125, 614.7559814453125, 151.86900329589844, 2156.22607421875, 504.42999267578125, 1388.950927734375, 767.2750244140625, 6749.38525390625]
Observed: nan, Expected: 0.0
215000.0
Length = 33
========================================================================
xs = 220000.0
Signal = [440.0, 1760.0, 14520.0, 44000.0, 82940.0, 62480.0, 20020.0, 10340.0, 6160.0, 4400.0, 3080.0, 2860.0, 2640.0, 440.0, 660.0, 2420.0, 1100.0, 880.0, 220.0, 1100.0, 440.0, 220.0, 220.0, 220.0, 220.0, 0.0, 0.0, 220.0, 0.0, 220.0, 220.0, 0.0, 1540.0]
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Bg unc + = [167951.671875, 430843.5, 639222.328125, 536962.96875, 522319.6875, 439450.359375, 347669.765625, 255748.1015625, 173211.4921875, 136528.20703125, 120343.5, 90157.154296875, 58076.255859375, 71602.470703125, 42669.6123046875, 44470.8896484375, 17827.224609375, 26903.2939453125, 12273.659912109375, 23676.755859375, 2632.8030395507812, 3980.6041259765625, 10302.602783203125, 6468.67822265625, 3088.409912109375, 8652.238037109375, 1844.2679443359375, 455.6070098876953, 6468.67822265625, 1513.2899780273438, 4166.852783203125, 2301.8250732421875, 20248.15576171875]
Bg unc - = [55983.890625, 143614.5, 213074.109375, 178987.65625, 174106.5625, 146483.453125, 115889.921875, 85249.3671875, 57737.1640625, 45509.40234375, 40114.5, 30052.384765625, 19358.751953125, 23867.490234375, 14223.2041015625, 14823.6298828125, 5942.408203125, 8967.7646484375, 4091.219970703125, 7892.251953125, 877.6010131835938, 1326.8680419921875, 3434.200927734375, 2156.22607421875, 1029.469970703125, 2884.079345703125, 614.7559814453125, 151.86900329589844, 2156.22607421875, 504.42999267578125, 1388.950927734375, 767.2750244140625, 6749.38525390625]
Observed: 0.0, Expected: 0.0
220000.0
Length = 33
========================================================================
xs = 225000.0
Signal = [450.0, 1800.0, 14850.0, 45000.0, 84825.0, 63900.0, 20475.0, 10575.0, 6300.0, 4500.0, 3150.0, 2925.0, 2700.0, 450.0, 675.0, 2475.0, 1125.0, 900.0, 225.0, 1125.0, 450.0, 225.0, 225.0, 225.0, 225.0, 0.0, 0.0, 225.0, 0.0, 225.0, 225.0, 0.0, 1575.0]
Bg = [111967.78125, 287229.0, 426148.21875, 357975.3125, 348213.125, 292966.90625, 231779.84375, 170498.734375, 115474.328125, 91018.8046875, 80229.0, 60104.76953125, 38717.50390625, 47734.98046875, 28446.408203125, 29647.259765625, 11884.81640625, 17935.529296875, 8182.43994140625, 15784.50390625, 1755.2020263671875, 2653.736083984375, 6868.40185546875, 4312.4521484375, 2058.93994140625, 5768.15869140625, 1229.511962890625, 303.7380065917969, 4312.4521484375, 1008.8599853515625, 2777.90185546875, 1534.550048828125, 13498.7705078125]
Bg unc + = [167951.671875, 430843.5, 639222.328125, 536962.96875, 522319.6875, 439450.359375, 347669.765625, 255748.1015625, 173211.4921875, 136528.20703125, 120343.5, 90157.154296875, 58076.255859375, 71602.470703125, 42669.6123046875, 44470.8896484375, 17827.224609375, 26903.2939453125, 12273.659912109375, 23676.755859375, 2632.8030395507812, 3980.6041259765625, 10302.602783203125, 6468.67822265625, 3088.409912109375, 8652.238037109375, 1844.2679443359375, 455.6070098876953, 6468.67822265625, 1513.2899780273438, 4166.852783203125, 2301.8250732421875, 20248.15576171875]
Bg unc - = [55983.890625, 143614.5, 213074.109375, 178987.65625, 174106.5625, 146483.453125, 115889.921875, 85249.3671875, 57737.1640625, 45509.40234375, 40114.5, 30052.384765625, 19358.751953125, 23867.490234375, 14223.2041015625, 14823.6298828125, 5942.408203125, 8967.7646484375, 4091.219970703125, 7892.251953125, 877.6010131835938, 1326.8680419921875, 3434.200927734375, 2156.22607421875, 1029.469970703125, 2884.079345703125, 614.7559814453125, 151.86900329589844, 2156.22607421875, 504.42999267578125, 1388.950927734375, 767.2750244140625, 6749.38525390625]
Observed: nan, Expected: 1.0
225000.0
Length = 33
========================================================================
xs = 230000.0
Signal = [460.0, 1840.0, 15180.0, 46000.0, 86710.0, 65320.0, 20930.0, 10810.0, 6440.0, 4600.0, 3220.0, 2990.0, 2760.0, 460.0, 690.0, 2530.0, 1150.0, 920.0, 230.0, 1150.0, 460.0, 230.0, 230.0, 230.0, 230.0, 0.0, 0.0, 230.0, 0.0, 230.0, 230.0, 0.0, 1610.0]
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Bg unc + = [167951.671875, 430843.5, 639222.328125, 536962.96875, 522319.6875, 439450.359375, 347669.765625, 255748.1015625, 173211.4921875, 136528.20703125, 120343.5, 90157.154296875, 58076.255859375, 71602.470703125, 42669.6123046875, 44470.8896484375, 17827.224609375, 26903.2939453125, 12273.659912109375, 23676.755859375, 2632.8030395507812, 3980.6041259765625, 10302.602783203125, 6468.67822265625, 3088.409912109375, 8652.238037109375, 1844.2679443359375, 455.6070098876953, 6468.67822265625, 1513.2899780273438, 4166.852783203125, 2301.8250732421875, 20248.15576171875]
Bg unc - = [55983.890625, 143614.5, 213074.109375, 178987.65625, 174106.5625, 146483.453125, 115889.921875, 85249.3671875, 57737.1640625, 45509.40234375, 40114.5, 30052.384765625, 19358.751953125, 23867.490234375, 14223.2041015625, 14823.6298828125, 5942.408203125, 8967.7646484375, 4091.219970703125, 7892.251953125, 877.6010131835938, 1326.8680419921875, 3434.200927734375, 2156.22607421875, 1029.469970703125, 2884.079345703125, 614.7559814453125, 151.86900329589844, 2156.22607421875, 504.42999267578125, 1388.950927734375, 767.2750244140625, 6749.38525390625]
Observed: 0.0, Expected: 0.0
230000.0
Length = 33
========================================================================
xs = 235000.0
Signal = [470.0, 1880.0, 15510.0, 47000.0, 88595.0, 66740.0, 21385.0, 11045.0, 6580.0, 4700.0, 3290.0, 3055.0, 2820.0, 470.0, 705.0, 2585.0, 1175.0, 940.0, 235.0, 1175.0, 470.0, 235.0, 235.0, 235.0, 235.0, 0.0, 0.0, 235.0, 0.0, 235.0, 235.0, 0.0, 1645.0]
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Bg unc + = [167951.671875, 430843.5, 639222.328125, 536962.96875, 522319.6875, 439450.359375, 347669.765625, 255748.1015625, 173211.4921875, 136528.20703125, 120343.5, 90157.154296875, 58076.255859375, 71602.470703125, 42669.6123046875, 44470.8896484375, 17827.224609375, 26903.2939453125, 12273.659912109375, 23676.755859375, 2632.8030395507812, 3980.6041259765625, 10302.602783203125, 6468.67822265625, 3088.409912109375, 8652.238037109375, 1844.2679443359375, 455.6070098876953, 6468.67822265625, 1513.2899780273438, 4166.852783203125, 2301.8250732421875, 20248.15576171875]
Bg unc - = [55983.890625, 143614.5, 213074.109375, 178987.65625, 174106.5625, 146483.453125, 115889.921875, 85249.3671875, 57737.1640625, 45509.40234375, 40114.5, 30052.384765625, 19358.751953125, 23867.490234375, 14223.2041015625, 14823.6298828125, 5942.408203125, 8967.7646484375, 4091.219970703125, 7892.251953125, 877.6010131835938, 1326.8680419921875, 3434.200927734375, 2156.22607421875, 1029.469970703125, 2884.079345703125, 614.7559814453125, 151.86900329589844, 2156.22607421875, 504.42999267578125, 1388.950927734375, 767.2750244140625, 6749.38525390625]
Observed: 0.0, Expected: 0.0
235000.0
Length = 33
========================================================================
xs = 240000.0
Signal = [480.0, 1920.0, 15840.0, 48000.0, 90480.0, 68160.0, 21840.0, 11280.0, 6720.0, 4800.0, 3360.0, 3120.0, 2880.0, 480.0, 720.0, 2640.0, 1200.0, 960.0, 240.0, 1200.0, 480.0, 240.0, 240.0, 240.0, 240.0, 0.0, 0.0, 240.0, 0.0, 240.0, 240.0, 0.0, 1680.0]
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Bg unc + = [167951.671875, 430843.5, 639222.328125, 536962.96875, 522319.6875, 439450.359375, 347669.765625, 255748.1015625, 173211.4921875, 136528.20703125, 120343.5, 90157.154296875, 58076.255859375, 71602.470703125, 42669.6123046875, 44470.8896484375, 17827.224609375, 26903.2939453125, 12273.659912109375, 23676.755859375, 2632.8030395507812, 3980.6041259765625, 10302.602783203125, 6468.67822265625, 3088.409912109375, 8652.238037109375, 1844.2679443359375, 455.6070098876953, 6468.67822265625, 1513.2899780273438, 4166.852783203125, 2301.8250732421875, 20248.15576171875]
Bg unc - = [55983.890625, 143614.5, 213074.109375, 178987.65625, 174106.5625, 146483.453125, 115889.921875, 85249.3671875, 57737.1640625, 45509.40234375, 40114.5, 30052.384765625, 19358.751953125, 23867.490234375, 14223.2041015625, 14823.6298828125, 5942.408203125, 8967.7646484375, 4091.219970703125, 7892.251953125, 877.6010131835938, 1326.8680419921875, 3434.200927734375, 2156.22607421875, 1029.469970703125, 2884.079345703125, 614.7559814453125, 151.86900329589844, 2156.22607421875, 504.42999267578125, 1388.950927734375, 767.2750244140625, 6749.38525390625]
Observed: 0.0, Expected: 0.0
240000.0
Length = 33
========================================================================
xs = 245000.0
Signal = [490.0, 1960.0, 16170.0, 49000.0, 92365.0, 69580.0, 22295.0, 11515.0, 6860.0, 4900.0, 3430.0, 3185.0, 2940.0, 490.0, 735.0, 2695.0, 1225.0, 980.0, 245.0, 1225.0, 490.0, 245.0, 245.0, 245.0, 245.0, 0.0, 0.0, 245.0, 0.0, 245.0, 245.0, 0.0, 1715.0]
Bg = [111967.78125, 287229.0, 426148.21875, 357975.3125, 348213.125, 292966.90625, 231779.84375, 170498.734375, 115474.328125, 91018.8046875, 80229.0, 60104.76953125, 38717.50390625, 47734.98046875, 28446.408203125, 29647.259765625, 11884.81640625, 17935.529296875, 8182.43994140625, 15784.50390625, 1755.2020263671875, 2653.736083984375, 6868.40185546875, 4312.4521484375, 2058.93994140625, 5768.15869140625, 1229.511962890625, 303.7380065917969, 4312.4521484375, 1008.8599853515625, 2777.90185546875, 1534.550048828125, 13498.7705078125]
Bg unc + = [167951.671875, 430843.5, 639222.328125, 536962.96875, 522319.6875, 439450.359375, 347669.765625, 255748.1015625, 173211.4921875, 136528.20703125, 120343.5, 90157.154296875, 58076.255859375, 71602.470703125, 42669.6123046875, 44470.8896484375, 17827.224609375, 26903.2939453125, 12273.659912109375, 23676.755859375, 2632.8030395507812, 3980.6041259765625, 10302.602783203125, 6468.67822265625, 3088.409912109375, 8652.238037109375, 1844.2679443359375, 455.6070098876953, 6468.67822265625, 1513.2899780273438, 4166.852783203125, 2301.8250732421875, 20248.15576171875]
Bg unc - = [55983.890625, 143614.5, 213074.109375, 178987.65625, 174106.5625, 146483.453125, 115889.921875, 85249.3671875, 57737.1640625, 45509.40234375, 40114.5, 30052.384765625, 19358.751953125, 23867.490234375, 14223.2041015625, 14823.6298828125, 5942.408203125, 8967.7646484375, 4091.219970703125, 7892.251953125, 877.6010131835938, 1326.8680419921875, 3434.200927734375, 2156.22607421875, 1029.469970703125, 2884.079345703125, 614.7559814453125, 151.86900329589844, 2156.22607421875, 504.42999267578125, 1388.950927734375, 767.2750244140625, 6749.38525390625]
Observed: 0.0, Expected: 0.0
245000.0
Length = 33
========================================================================
xs = 250000.0
Signal = [500.0, 2000.0, 16500.0, 50000.0, 94250.0, 71000.0, 22750.0, 11750.0, 7000.0, 5000.0, 3500.0, 3250.0, 3000.0, 500.0, 750.0, 2750.0, 1250.0, 1000.0, 250.0, 1250.0, 500.0, 250.0, 250.0, 250.0, 250.0, 0.0, 0.0, 250.0, 0.0, 250.0, 250.0, 0.0, 1750.0]
Bg = [111967.78125, 287229.0, 426148.21875, 357975.3125, 348213.125, 292966.90625, 231779.84375, 170498.734375, 115474.328125, 91018.8046875, 80229.0, 60104.76953125, 38717.50390625, 47734.98046875, 28446.408203125, 29647.259765625, 11884.81640625, 17935.529296875, 8182.43994140625, 15784.50390625, 1755.2020263671875, 2653.736083984375, 6868.40185546875, 4312.4521484375, 2058.93994140625, 5768.15869140625, 1229.511962890625, 303.7380065917969, 4312.4521484375, 1008.8599853515625, 2777.90185546875, 1534.550048828125, 13498.7705078125]
Bg unc + = [167951.671875, 430843.5, 639222.328125, 536962.96875, 522319.6875, 439450.359375, 347669.765625, 255748.1015625, 173211.4921875, 136528.20703125, 120343.5, 90157.154296875, 58076.255859375, 71602.470703125, 42669.6123046875, 44470.8896484375, 17827.224609375, 26903.2939453125, 12273.659912109375, 23676.755859375, 2632.8030395507812, 3980.6041259765625, 10302.602783203125, 6468.67822265625, 3088.409912109375, 8652.238037109375, 1844.2679443359375, 455.6070098876953, 6468.67822265625, 1513.2899780273438, 4166.852783203125, 2301.8250732421875, 20248.15576171875]
Bg unc - = [55983.890625, 143614.5, 213074.109375, 178987.65625, 174106.5625, 146483.453125, 115889.921875, 85249.3671875, 57737.1640625, 45509.40234375, 40114.5, 30052.384765625, 19358.751953125, 23867.490234375, 14223.2041015625, 14823.6298828125, 5942.408203125, 8967.7646484375, 4091.219970703125, 7892.251953125, 877.6010131835938, 1326.8680419921875, 3434.200927734375, 2156.22607421875, 1029.469970703125, 2884.079345703125, 614.7559814453125, 151.86900329589844, 2156.22607421875, 504.42999267578125, 1388.950927734375, 767.2750244140625, 6749.38525390625]
Observed: nan, Expected: 1.0
250000.0
Length = 33
========================================================================
xs = 255000.0
Signal = [510.0, 2040.0, 16830.0, 51000.0, 96135.0, 72420.0, 23205.0, 11985.0, 7140.0, 5100.0, 3570.0, 3315.0, 3060.0, 510.0, 765.0, 2805.0, 1275.0, 1020.0, 255.0, 1275.0, 510.0, 255.0, 255.0, 255.0, 255.0, 0.0, 0.0, 255.0, 0.0, 255.0, 255.0, 0.0, 1785.0]
Bg = [111967.78125, 287229.0, 426148.21875, 357975.3125, 348213.125, 292966.90625, 231779.84375, 170498.734375, 115474.328125, 91018.8046875, 80229.0, 60104.76953125, 38717.50390625, 47734.98046875, 28446.408203125, 29647.259765625, 11884.81640625, 17935.529296875, 8182.43994140625, 15784.50390625, 1755.2020263671875, 2653.736083984375, 6868.40185546875, 4312.4521484375, 2058.93994140625, 5768.15869140625, 1229.511962890625, 303.7380065917969, 4312.4521484375, 1008.8599853515625, 2777.90185546875, 1534.550048828125, 13498.7705078125]
Bg unc + = [167951.671875, 430843.5, 639222.328125, 536962.96875, 522319.6875, 439450.359375, 347669.765625, 255748.1015625, 173211.4921875, 136528.20703125, 120343.5, 90157.154296875, 58076.255859375, 71602.470703125, 42669.6123046875, 44470.8896484375, 17827.224609375, 26903.2939453125, 12273.659912109375, 23676.755859375, 2632.8030395507812, 3980.6041259765625, 10302.602783203125, 6468.67822265625, 3088.409912109375, 8652.238037109375, 1844.2679443359375, 455.6070098876953, 6468.67822265625, 1513.2899780273438, 4166.852783203125, 2301.8250732421875, 20248.15576171875]
Bg unc - = [55983.890625, 143614.5, 213074.109375, 178987.65625, 174106.5625, 146483.453125, 115889.921875, 85249.3671875, 57737.1640625, 45509.40234375, 40114.5, 30052.384765625, 19358.751953125, 23867.490234375, 14223.2041015625, 14823.6298828125, 5942.408203125, 8967.7646484375, 4091.219970703125, 7892.251953125, 877.6010131835938, 1326.8680419921875, 3434.200927734375, 2156.22607421875, 1029.469970703125, 2884.079345703125, 614.7559814453125, 151.86900329589844, 2156.22607421875, 504.42999267578125, 1388.950927734375, 767.2750244140625, 6749.38525390625]
Observed: 0.5, Expected: 0.0
255000.0
Length = 33
========================================================================
xs = 260000.0
Signal = [520.0, 2080.0, 17160.0, 52000.0, 98020.0, 73840.0, 23660.0, 12220.0, 7280.0, 5200.0, 3640.0, 3380.0, 3120.0, 520.0, 780.0, 2860.0, 1300.0, 1040.0, 260.0, 1300.0, 520.0, 260.0, 260.0, 260.0, 260.0, 0.0, 0.0, 260.0, 0.0, 260.0, 260.0, 0.0, 1820.0]
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Observed: 0.0, Expected: 0.0
260000.0
Length = 33
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xs = 265000.0
Signal = [530.0, 2120.0, 17490.0, 53000.0, 99905.0, 75260.0, 24115.0, 12455.0, 7420.0, 5300.0, 3710.0, 3445.0, 3180.0, 530.0, 795.0, 2915.0, 1325.0, 1060.0, 265.0, 1325.0, 530.0, 265.0, 265.0, 265.0, 265.0, 0.0, 0.0, 265.0, 0.0, 265.0, 265.0, 0.0, 1855.0]
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Bg unc + = [167951.671875, 430843.5, 639222.328125, 536962.96875, 522319.6875, 439450.359375, 347669.765625, 255748.1015625, 173211.4921875, 136528.20703125, 120343.5, 90157.154296875, 58076.255859375, 71602.470703125, 42669.6123046875, 44470.8896484375, 17827.224609375, 26903.2939453125, 12273.659912109375, 23676.755859375, 2632.8030395507812, 3980.6041259765625, 10302.602783203125, 6468.67822265625, 3088.409912109375, 8652.238037109375, 1844.2679443359375, 455.6070098876953, 6468.67822265625, 1513.2899780273438, 4166.852783203125, 2301.8250732421875, 20248.15576171875]
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Observed: nan, Expected: 0.0
265000.0
Length = 33
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xs = 270000.0
Signal = [540.0, 2160.0, 17820.0, 54000.0, 101790.0, 76680.0, 24570.0, 12690.0, 7560.0, 5400.0, 3780.0, 3510.0, 3240.0, 540.0, 810.0, 2970.0, 1350.0, 1080.0, 270.0, 1350.0, 540.0, 270.0, 270.0, 270.0, 270.0, 0.0, 0.0, 270.0, 0.0, 270.0, 270.0, 0.0, 1890.0]
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Bg unc + = [167951.671875, 430843.5, 639222.328125, 536962.96875, 522319.6875, 439450.359375, 347669.765625, 255748.1015625, 173211.4921875, 136528.20703125, 120343.5, 90157.154296875, 58076.255859375, 71602.470703125, 42669.6123046875, 44470.8896484375, 17827.224609375, 26903.2939453125, 12273.659912109375, 23676.755859375, 2632.8030395507812, 3980.6041259765625, 10302.602783203125, 6468.67822265625, 3088.409912109375, 8652.238037109375, 1844.2679443359375, 455.6070098876953, 6468.67822265625, 1513.2899780273438, 4166.852783203125, 2301.8250732421875, 20248.15576171875]
Bg unc - = [55983.890625, 143614.5, 213074.109375, 178987.65625, 174106.5625, 146483.453125, 115889.921875, 85249.3671875, 57737.1640625, 45509.40234375, 40114.5, 30052.384765625, 19358.751953125, 23867.490234375, 14223.2041015625, 14823.6298828125, 5942.408203125, 8967.7646484375, 4091.219970703125, 7892.251953125, 877.6010131835938, 1326.8680419921875, 3434.200927734375, 2156.22607421875, 1029.469970703125, 2884.079345703125, 614.7559814453125, 151.86900329589844, 2156.22607421875, 504.42999267578125, 1388.950927734375, 767.2750244140625, 6749.38525390625]
Observed: 0.0, Expected: 0.0
270000.0
Length = 33
========================================================================
xs = 275000.0
Signal = [550.0, 2200.0, 18150.0, 55000.0, 103675.0, 78100.0, 25025.0, 12925.0, 7700.0, 5500.0, 3850.0, 3575.0, 3300.0, 550.0, 825.0, 3025.0, 1375.0, 1100.0, 275.0, 1375.0, 550.0, 275.0, 275.0, 275.0, 275.0, 0.0, 0.0, 275.0, 0.0, 275.0, 275.0, 0.0, 1925.0]
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Observed: 0.0, Expected: 0.0
275000.0
Length = 33
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xs = 280000.0
Signal = [560.0, 2240.0, 18480.0, 56000.0, 105560.0, 79520.0, 25480.0, 13160.0, 7840.0, 5600.0, 3920.0, 3640.0, 3360.0, 560.0, 840.0, 3080.0, 1400.0, 1120.0, 280.0, 1400.0, 560.0, 280.0, 280.0, 280.0, 280.0, 0.0, 0.0, 280.0, 0.0, 280.0, 280.0, 0.0, 1960.0]
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Bg unc - = [55983.890625, 143614.5, 213074.109375, 178987.65625, 174106.5625, 146483.453125, 115889.921875, 85249.3671875, 57737.1640625, 45509.40234375, 40114.5, 30052.384765625, 19358.751953125, 23867.490234375, 14223.2041015625, 14823.6298828125, 5942.408203125, 8967.7646484375, 4091.219970703125, 7892.251953125, 877.6010131835938, 1326.8680419921875, 3434.200927734375, 2156.22607421875, 1029.469970703125, 2884.079345703125, 614.7559814453125, 151.86900329589844, 2156.22607421875, 504.42999267578125, 1388.950927734375, 767.2750244140625, 6749.38525390625]
Observed: 1.0, Expected: 1.0
280000.0
Length = 33
========================================================================
xs = 285000.0
Signal = [570.0, 2280.0, 18810.0, 57000.0, 107445.0, 80940.0, 25935.0, 13395.0, 7980.0, 5700.0, 3990.0, 3705.0, 3420.0, 570.0, 855.0, 3135.0, 1425.0, 1140.0, 285.0, 1425.0, 570.0, 285.0, 285.0, 285.0, 285.0, 0.0, 0.0, 285.0, 0.0, 285.0, 285.0, 0.0, 1995.0]
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Bg unc + = [167951.671875, 430843.5, 639222.328125, 536962.96875, 522319.6875, 439450.359375, 347669.765625, 255748.1015625, 173211.4921875, 136528.20703125, 120343.5, 90157.154296875, 58076.255859375, 71602.470703125, 42669.6123046875, 44470.8896484375, 17827.224609375, 26903.2939453125, 12273.659912109375, 23676.755859375, 2632.8030395507812, 3980.6041259765625, 10302.602783203125, 6468.67822265625, 3088.409912109375, 8652.238037109375, 1844.2679443359375, 455.6070098876953, 6468.67822265625, 1513.2899780273438, 4166.852783203125, 2301.8250732421875, 20248.15576171875]
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Observed: 0.0, Expected: 0.0
285000.0
Length = 33
========================================================================
xs = 290000.0
Signal = [580.0, 2320.0, 19140.0, 58000.0, 109330.0, 82360.0, 26390.0, 13630.0, 8120.0, 5800.0, 4060.0, 3770.0, 3480.0, 580.0, 870.0, 3190.0, 1450.0, 1160.0, 290.0, 1450.0, 580.0, 290.0, 290.0, 290.0, 290.0, 0.0, 0.0, 290.0, 0.0, 290.0, 290.0, 0.0, 2030.0]
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Bg unc + = [167951.671875, 430843.5, 639222.328125, 536962.96875, 522319.6875, 439450.359375, 347669.765625, 255748.1015625, 173211.4921875, 136528.20703125, 120343.5, 90157.154296875, 58076.255859375, 71602.470703125, 42669.6123046875, 44470.8896484375, 17827.224609375, 26903.2939453125, 12273.659912109375, 23676.755859375, 2632.8030395507812, 3980.6041259765625, 10302.602783203125, 6468.67822265625, 3088.409912109375, 8652.238037109375, 1844.2679443359375, 455.6070098876953, 6468.67822265625, 1513.2899780273438, 4166.852783203125, 2301.8250732421875, 20248.15576171875]
Bg unc - = [55983.890625, 143614.5, 213074.109375, 178987.65625, 174106.5625, 146483.453125, 115889.921875, 85249.3671875, 57737.1640625, 45509.40234375, 40114.5, 30052.384765625, 19358.751953125, 23867.490234375, 14223.2041015625, 14823.6298828125, 5942.408203125, 8967.7646484375, 4091.219970703125, 7892.251953125, 877.6010131835938, 1326.8680419921875, 3434.200927734375, 2156.22607421875, 1029.469970703125, 2884.079345703125, 614.7559814453125, 151.86900329589844, 2156.22607421875, 504.42999267578125, 1388.950927734375, 767.2750244140625, 6749.38525390625]
Observed: 0.5, Expected: 0.0
290000.0
Length = 33
========================================================================
xs = 295000.0
Signal = [590.0, 2360.0, 19470.0, 59000.0, 111215.0, 83780.0, 26845.0, 13865.0, 8260.0, 5900.0, 4130.0, 3835.0, 3540.0, 590.0, 885.0, 3245.0, 1475.0, 1180.0, 295.0, 1475.0, 590.0, 295.0, 295.0, 295.0, 295.0, 0.0, 0.0, 295.0, 0.0, 295.0, 295.0, 0.0, 2065.0]
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Bg unc + = [167951.671875, 430843.5, 639222.328125, 536962.96875, 522319.6875, 439450.359375, 347669.765625, 255748.1015625, 173211.4921875, 136528.20703125, 120343.5, 90157.154296875, 58076.255859375, 71602.470703125, 42669.6123046875, 44470.8896484375, 17827.224609375, 26903.2939453125, 12273.659912109375, 23676.755859375, 2632.8030395507812, 3980.6041259765625, 10302.602783203125, 6468.67822265625, 3088.409912109375, 8652.238037109375, 1844.2679443359375, 455.6070098876953, 6468.67822265625, 1513.2899780273438, 4166.852783203125, 2301.8250732421875, 20248.15576171875]
Bg unc - = [55983.890625, 143614.5, 213074.109375, 178987.65625, 174106.5625, 146483.453125, 115889.921875, 85249.3671875, 57737.1640625, 45509.40234375, 40114.5, 30052.384765625, 19358.751953125, 23867.490234375, 14223.2041015625, 14823.6298828125, 5942.408203125, 8967.7646484375, 4091.219970703125, 7892.251953125, 877.6010131835938, 1326.8680419921875, 3434.200927734375, 2156.22607421875, 1029.469970703125, 2884.079345703125, 614.7559814453125, 151.86900329589844, 2156.22607421875, 504.42999267578125, 1388.950927734375, 767.2750244140625, 6749.38525390625]
Observed: 1.0, Expected: 1.0
295000.0
Length = 33
========================================================================
xs = 300000.0
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Hi all -- thanks for your help so far. Let me know if I can provide any more info to help you find the source of this, or if I'm misusing the model. Daniel |
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@danielwhiteson Sorry for the delay in responding to you — I'm traveling this week and so many things are falling behind. |
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@danielwhiteson Yes, sorry for the very slow response here. For details that I won't get into the last weeks have pulled us away from being able to do much here beyond try to queue up a patch release. Let me take another look at this tonight and actually give some thought to what you're doing. |
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I'm going to have to poke at this in more depth the evening of 2023-04-05 as after paper reviews tonight I don't see anything super obvious and small perturbations change the behavior. |
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One thing one could try is to replace the Poissons w/ Gaussians.. the yields are so large, that maybe there are numerical issues - there is no easy way to do this within |
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Did you have a chance to take a look? |
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Hi all,
I think that intuition is smart. The issue appears when the bin counts grow large.
Daniel
… On Apr 7, 2023, at 12:00 PM, Lukas ***@***.***> wrote:
One thing one could try is to replace the Poissons w/ Gaussians.. the yields are so large, that maybe there are numerical issues - there is no easy way to do this within pyhf out of the box, but should not be too horrible to code up
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Hi all -- any progress on this issue? |
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Hi -- is this still active, or should I assume the issue will not be resolved soon? |
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👋 @danielwhiteson. Open, so still active, but given the core devs travel schedules this month this may or may not be resolved by the end of July. Next week is PyHEP.dev and while the focus of that won't be coding sprints per say it may offer some time to work through a backlog of issues and questions (this one included). |
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A student of mine is using pyhf to set some limits. He is running to a weird issue which only crops up if he has too few bins. If the number of bins gets small, so the number of events in the bins grows large, he starts to get nans and nonsense results.
Example output and a script that reproduces it is below. Are we doing something obviously wrong?
Daniel
log.txt
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