From d7075ed3efc0a3a7c599e93995c22fdabfa1e474 Mon Sep 17 00:00:00 2001 From: Andrey Pozdnyakov Date: Wed, 28 Mar 2018 15:54:37 +0200 Subject: [PATCH 01/12] Toy study --- toyStudy/README.md | 29 ++++++++ toyStudy/card_cut_n_count.txt | 16 +++++ toyStudy/card_shape_n_roll.txt | 24 +++++++ toyStudy/fig_cut_n_count.png | Bin 0 -> 30118 bytes toyStudy/fig_gen_bkg.png | Bin 0 -> 14878 bytes toyStudy/fig_scale_with_sigma.png | Bin 0 -> 47342 bytes toyStudy/hhbbgg.inputbkg_13TeV.root | Bin 0 -> 31651 bytes toyStudy/readWS.py | 34 ++++++++++ toyStudy/toyLimit_cut_n_count.py | 69 +++++++++++++++++++ toyStudy/toyLimit_shape_n_roll.py | 100 ++++++++++++++++++++++++++++ 10 files changed, 272 insertions(+) create mode 100644 toyStudy/README.md create mode 100644 toyStudy/card_cut_n_count.txt create mode 100644 toyStudy/card_shape_n_roll.txt create mode 100644 toyStudy/fig_cut_n_count.png create mode 100644 toyStudy/fig_gen_bkg.png create mode 100644 toyStudy/fig_scale_with_sigma.png create mode 100644 toyStudy/hhbbgg.inputbkg_13TeV.root create mode 100644 toyStudy/readWS.py create mode 100644 toyStudy/toyLimit_cut_n_count.py create mode 100644 toyStudy/toyLimit_shape_n_roll.py diff --git a/toyStudy/README.md b/toyStudy/README.md new file mode 100644 index 0000000..3ce1e64 --- /dev/null +++ b/toyStudy/README.md @@ -0,0 +1,29 @@ +## How to play this toy + +### Cut and count + +A template card for this game is [card_cut_n_count.txt](card_cut_n_count.txt), in which +the strings `%SIG%` and `%BKG%` will be replaced in a script. +The corresponding script is [toyLimit_cut_n_count.py](toyLimit_cut_n_count.py). Just run it: + +``` python toyLimit_cut_n_count.py ``` +You will get a plot like this: +![Cut-n-count results](fig_cut_n_count.png) + +### Play with shapes + +Template card for this game is [card_shape_n_roll.txt](card_shape_n_roll.txt). Here we +will be replacing `%SIG%`, `%BKG%` and `%SW%` within [toyLimit_shape_n_roll.py](toyLimit_shape_n_roll.py) script. + +``` python toyLimit_shape_n_roll.py ``` + +You will get a plot like this, which shows how the limits scale with the width of the gaussian: +![Shape results](fig_scale_with_sigma.png) + + +And here are the toys generated for that game: +![Toy data](fig_gen_bkg.png) + + + + diff --git a/toyStudy/card_cut_n_count.txt b/toyStudy/card_cut_n_count.txt new file mode 100644 index 0000000..d12be36 --- /dev/null +++ b/toyStudy/card_cut_n_count.txt @@ -0,0 +1,16 @@ +imax 1 +jmax 1 +kmax * + +bin bin1 +observation 5 + +bin bin1 bin1 +process sig bkg +process 0 1 +rate %SIG% %BKG% + + +lumi lnN 1.03 - +sig_sys lnN 1.10 - +bkg_sys lnN - 1.10 diff --git a/toyStudy/card_shape_n_roll.txt b/toyStudy/card_shape_n_roll.txt new file mode 100644 index 0000000..f5e1de6 --- /dev/null +++ b/toyStudy/card_shape_n_roll.txt @@ -0,0 +1,24 @@ +imax 1 +jmax 1 +kmax * +--------------- +#shapes 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z#~ArP=*9o8sq@d8Apak}#Xq0@@4GPnEb9DU)G+@y>i-P0e*h={%TfP8S-c9}*pq<% E4*+mX!2kdN literal 0 HcmV?d00001 diff --git a/toyStudy/readWS.py b/toyStudy/readWS.py new file mode 100644 index 0000000..b6b5ce6 --- /dev/null +++ b/toyStudy/readWS.py @@ -0,0 +1,34 @@ +#! /usr/bin/env python +import os,sys, argparse, time +import tempfile, getpass, subprocess +import numpy as np +import matplotlib.pyplot as plt + +username = getpass.getuser() +from ROOT import * +gROOT.SetBatch() + + +# Get the shape of the background from a real card +rooWsFile = TFile('hhbbgg.inputbkg_13TeV.root') +anaWs = rooWsFile.Get('w_all') +anaWs.Print() + +mgg = anaWs.var('mgg') +mgg.Print() + +anaBkgPdf = anaWs.pdf("mggBkgTmpBer1_cat0_CMS_Bkg_cat2") +fakeData = anaBkgPdf.generate(RooArgSet(mgg), 120) + +anaBkgPdf.Print() + +c = TCanvas("c","c",0,0,900,600) +c.cd() + + +testFrame = mgg.frame() +fakeData.plotOn(testFrame, RooFit.Binning(80), RooFit.Name('data1')) +anaBkgPdf.plotOn(testFrame, RooFit.Name("Bkg"), RooFit.LineColor(kBlue), RooFit.LineWidth(2), RooFit.FillColor(kCyan-6)) +testFrame.Draw() + +c.SaveAs('fig_ana.png') diff --git a/toyStudy/toyLimit_cut_n_count.py b/toyStudy/toyLimit_cut_n_count.py new file mode 100644 index 0000000..9aaf7d6 --- /dev/null +++ b/toyStudy/toyLimit_cut_n_count.py @@ -0,0 +1,69 @@ +#! /usr/bin/env python +import os,sys, argparse, time +import tempfile, getpass, subprocess +import numpy as np +import matplotlib.pyplot as plt + +username = getpass.getuser() +from ROOT import * +gROOT.SetBatch() + +Ns = np.array([2,2.5,3,3.5,4,4.5,5,6,8,10,15,20,30]) +Ss = np.array([2, 4, 6]) + +toyCard1 = 'card_cut_n_count.txt' +processes = [] + +with open(toyCard1, 'r') as templateCard: + tmpCard = templateCard.read() + for si in Ss: + for N in Ns: + with tempfile.NamedTemporaryFile(dir='/tmp/'+username, prefix='toyCard_N'+str(N), suffix='.txt', delete=False) as card: + newCard = tmpCard.replace('%BKG%',str(N)).replace('%SIG%',str(si)) + print N + #print newCard + + card.write(newCard) + print card.name + pro = subprocess.Popen(['combine','-M','Asymptotic', '-m', '125','-n','_CutCount_NBKG_'+str(N)+'_NSIG_'+str(si), card.name]) + processes.append(pro) + time.sleep(0.2) + +# Wait till all processes are finished: +for p in processes: + print 'waiting for', p + p.wait() + +# Now open output files and read the limit values: + +limsAll = {} + +for si in Ss: + lims = [] + for N in Ns: + fname = 'higgsCombine_CutCount_NBKG_'+str(N)+'_NSIG_'+str(si)+'.Asymptotic.mH125.root' + rfile = TFile(fname, 'READ') + tree = rfile.Get("limit") + tree.Draw("limit:quantileExpected", "", "goff") + + #for v in range(0, tree.GetSelectedRows()): + # print v, tree.GetV1()[v], tree.GetV2()[v] + # Quantiles are: [0]=0.025, [1]=0.16, [2]=0.5, [3]0.84, [4]=0.875, [5]=-1 (observed) + lims.append(tree.GetV1()[2]) + rfile.Close() + print N, lims[-1] + limsAll[str(si)] = lims + + print 'Expected limit at r=0.5: ', lims +print limsAll + +plt.plot(np.sqrt(Ns), limsAll['2'], 'ro', label="Sig = 2 Ev") +plt.plot(np.sqrt(Ns), limsAll['4'], 'bs', label="Sig = 4 Ev") +plt.plot(np.sqrt(Ns), limsAll['6'], 'g^', label="Sig = 6 Ev") +plt.axis([0, 8, 0, 8]) +plt.title('Limits from toy counting experiments') +plt.xlabel(r'$\sqrt{N_{bkg}}$') +plt.ylabel('Median expected Limit') +plt.legend() + +plt.savefig('fig_cut_n_count.png') diff --git a/toyStudy/toyLimit_shape_n_roll.py b/toyStudy/toyLimit_shape_n_roll.py new file mode 100644 index 0000000..3b54fa5 --- /dev/null +++ b/toyStudy/toyLimit_shape_n_roll.py @@ -0,0 +1,100 @@ +#! /usr/bin/env python +import os,sys, argparse, time +import tempfile, getpass, subprocess +import numpy as np +import matplotlib.pyplot as plt + +username = getpass.getuser() +from ROOT import * +gROOT.SetBatch() + + + +c = TCanvas("c","c",0,0,900,600) +c.cd() + +w = RooWorkspace("w") +w.factory('Gaussian::sig(x[100,180],mu[125],sigma[1])') +w.factory('Exponential::bkg(x,tau[-0.04])') +#w.factory('Chebychev::bkg(x,{-0.4,0.1})') +w.Print() + +x = w.var('x') +sigPdf = w.pdf("sig") +bkgPdf = w.pdf("bkg") +fakeData2 = bkgPdf.generate(RooArgSet(x), 120) +getattr(w,'import')(fakeData2,RooFit.Rename("data_obs")) + +testFrame = x.frame() +fakeData2.plotOn(testFrame, RooFit.Binning(80), RooFit.Name('data2')) +bkgPdf.plotOn(testFrame, RooFit.Name("Bkg 2"), RooFit.LineColor(kBlue), RooFit.LineWidth(2), RooFit.FillColor(kCyan-6)) +sigPdf.plotOn(testFrame, RooFit.Name("fake sig"), RooFit.LineColor(kRed+2), RooFit.LineWidth(2), RooFit.Normalization(0.10)) +testFrame.Draw() + +c.SaveAs('fig_gen_bkg.png') + +w.writeToFile('ws.root') + +Sigmas = np.array([0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 2.0]) +Ns = np.array([100,120]) +Ss = np.array([2, 4, 6]) +toyCard2 = 'card_shape_n_roll.txt' + + +processes = [] +for sw in Sigmas: + with open(toyCard2, 'r') as templateCard: + tmpCard = templateCard.read() + for si in Ss: + for N in Ns: + with tempfile.NamedTemporaryFile(dir='/tmp/'+username, prefix='toyCard_N'+str(N), suffix='.txt', delete=False) as card: + newCard = tmpCard.replace('%BKG%',str(N)).replace('%SIG%',str(si)).replace('%SW%',str(sw)) + + card.write(newCard) + print card.name + pro = subprocess.Popen(['combine','-M','Asymptotic', '-m', '125','-n','_Shape_NBKG_'+str(N)+'_NSIG_'+str(si)+'_sw_'+str(sw), card.name]) + processes.append(pro) + time.sleep(0.2) + + +# Wait till all processes are finished: +for p in processes: + print 'waiting for', p + p.wait() + + + +limsAll = {} + +for si in Ss: + for N in Ns: + lims = [] + for sw in Sigmas: + fname = 'higgsCombine_Shape_NBKG_'+str(N)+'_NSIG_'+str(si)+'_sw_'+str(sw)+'.Asymptotic.mH125.root' + rfile = TFile(fname, 'READ') + tree = rfile.Get("limit") + tree.Draw("limit:quantileExpected", "", "goff") + + lims.append(tree.GetV1()[2]) + rfile.Close() + # print si, N, sw, lims[-1] + limsAll['NBKG_'+str(N)+'_NSIG_'+str(si)] = lims + + #print 'Expected limit at r=0.5: ', lims +print limsAll + + +import itertools +marker = itertools.cycle((',', '+', '.', 'o', '*', '^')) + +plt.clf() +for si in Ss: + for N in Ns: + plt.plot(np.sqrt(Sigmas), limsAll['NBKG_'+str(N)+'_NSIG_'+str(si)], marker = marker.next(), label='$N_{bkg} = '+str(N)+'; N_{sig} = '+str(si)+'$') +plt.axis([0.5, 2.5, 0, 8]) +plt.title('Limits from toy shapes') +plt.xlabel(r'$\sqrt{\sigma_{eff}(signal)}}$') +plt.ylabel('Median expected Limit') +plt.legend() +plt.savefig('fig_scale_with_sigma.png') + From 520e92ec4a4d876a660198f72697c0d532428352 Mon Sep 17 00:00:00 2001 From: Andrey Pozdnyakov Date: Wed, 28 Mar 2018 16:00:34 +0200 Subject: [PATCH 02/12] Renaming variables for readability --- toyStudy/README.md | 1 + toyStudy/toyLimit_cut_n_count.py | 18 +++++++++--------- toyStudy/toyLimit_shape_n_roll.py | 16 ++++++++-------- 3 files changed, 18 insertions(+), 17 deletions(-) diff --git a/toyStudy/README.md b/toyStudy/README.md index 3ce1e64..ad72819 100644 --- a/toyStudy/README.md +++ b/toyStudy/README.md @@ -7,6 +7,7 @@ the strings `%SIG%` and `%BKG%` will be replaced in a script. The corresponding script is [toyLimit_cut_n_count.py](toyLimit_cut_n_count.py). Just run it: ``` python toyLimit_cut_n_count.py ``` + You will get a plot like this: ![Cut-n-count results](fig_cut_n_count.png) diff --git a/toyStudy/toyLimit_cut_n_count.py b/toyStudy/toyLimit_cut_n_count.py index 9aaf7d6..76fe81a 100644 --- a/toyStudy/toyLimit_cut_n_count.py +++ b/toyStudy/toyLimit_cut_n_count.py @@ -8,16 +8,16 @@ from ROOT import * gROOT.SetBatch() -Ns = np.array([2,2.5,3,3.5,4,4.5,5,6,8,10,15,20,30]) -Ss = np.array([2, 4, 6]) +Nbkg = np.array([2,2.5,3,3.5,4,4.5,5,6,8,10,15,20,30]) +Nsig = np.array([2, 4, 6]) toyCard1 = 'card_cut_n_count.txt' processes = [] with open(toyCard1, 'r') as templateCard: tmpCard = templateCard.read() - for si in Ss: - for N in Ns: + for si in Nsig: + for N in Nbkg: with tempfile.NamedTemporaryFile(dir='/tmp/'+username, prefix='toyCard_N'+str(N), suffix='.txt', delete=False) as card: newCard = tmpCard.replace('%BKG%',str(N)).replace('%SIG%',str(si)) print N @@ -38,9 +38,9 @@ limsAll = {} -for si in Ss: +for si in Nsig: lims = [] - for N in Ns: + for N in Nbkg: fname = 'higgsCombine_CutCount_NBKG_'+str(N)+'_NSIG_'+str(si)+'.Asymptotic.mH125.root' rfile = TFile(fname, 'READ') tree = rfile.Get("limit") @@ -57,9 +57,9 @@ print 'Expected limit at r=0.5: ', lims print limsAll -plt.plot(np.sqrt(Ns), limsAll['2'], 'ro', label="Sig = 2 Ev") -plt.plot(np.sqrt(Ns), limsAll['4'], 'bs', label="Sig = 4 Ev") -plt.plot(np.sqrt(Ns), limsAll['6'], 'g^', label="Sig = 6 Ev") +plt.plot(np.sqrt(Nbkg), limsAll['2'], 'ro', label="Sig = 2 Ev") +plt.plot(np.sqrt(Nbkg), limsAll['4'], 'bs', label="Sig = 4 Ev") +plt.plot(np.sqrt(Nbkg), limsAll['6'], 'g^', label="Sig = 6 Ev") plt.axis([0, 8, 0, 8]) plt.title('Limits from toy counting experiments') plt.xlabel(r'$\sqrt{N_{bkg}}$') diff --git a/toyStudy/toyLimit_shape_n_roll.py b/toyStudy/toyLimit_shape_n_roll.py index 3b54fa5..25b1cf2 100644 --- a/toyStudy/toyLimit_shape_n_roll.py +++ b/toyStudy/toyLimit_shape_n_roll.py @@ -36,8 +36,8 @@ w.writeToFile('ws.root') Sigmas = np.array([0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 2.0]) -Ns = np.array([100,120]) -Ss = np.array([2, 4, 6]) +Nbkg = np.array([100,120]) +Nsig = np.array([2, 4, 6]) toyCard2 = 'card_shape_n_roll.txt' @@ -45,8 +45,8 @@ for sw in Sigmas: with open(toyCard2, 'r') as templateCard: tmpCard = templateCard.read() - for si in Ss: - for N in Ns: + for si in Nsig: + for N in Nbkg: with tempfile.NamedTemporaryFile(dir='/tmp/'+username, prefix='toyCard_N'+str(N), suffix='.txt', delete=False) as card: newCard = tmpCard.replace('%BKG%',str(N)).replace('%SIG%',str(si)).replace('%SW%',str(sw)) @@ -66,8 +66,8 @@ limsAll = {} -for si in Ss: - for N in Ns: +for si in Nsig: + for N in Nbkg: lims = [] for sw in Sigmas: fname = 'higgsCombine_Shape_NBKG_'+str(N)+'_NSIG_'+str(si)+'_sw_'+str(sw)+'.Asymptotic.mH125.root' @@ -88,8 +88,8 @@ marker = itertools.cycle((',', '+', '.', 'o', '*', '^')) plt.clf() -for si in Ss: - for N in Ns: +for si in Nsig: + for N in Nbkg: plt.plot(np.sqrt(Sigmas), limsAll['NBKG_'+str(N)+'_NSIG_'+str(si)], marker = marker.next(), label='$N_{bkg} = '+str(N)+'; N_{sig} = '+str(si)+'$') plt.axis([0.5, 2.5, 0, 8]) plt.title('Limits from toy shapes') From 42ac50e5fc6cf35846f995083c297a7fbae8d3e4 Mon Sep 17 00:00:00 2001 From: Andrey Pozdnyakov Date: Sat, 31 Mar 2018 15:44:42 +0200 Subject: [PATCH 03/12] Table for cut n count --- README.md | 4 - toyStudy/README.md | 28 ++++- toyStudy/fig_cut_n_count.png | Bin 30118 -> 0 bytes toyStudy/figs/fig_cut_n_count.png | Bin 0 -> 32509 bytes toyStudy/{ => figs}/fig_gen_bkg.png | Bin toyStudy/{ => figs}/fig_scale_with_sigma.png | Bin toyStudy/readWS.py | 120 ++++++++++++++++--- toyStudy/toyLimit_cut_n_count.py | 53 ++++++-- toyStudy/toyLimit_shape_n_roll.py | 32 +++-- 9 files changed, 190 insertions(+), 47 deletions(-) delete mode 100644 toyStudy/fig_cut_n_count.png create mode 100644 toyStudy/figs/fig_cut_n_count.png rename toyStudy/{ => figs}/fig_gen_bkg.png (100%) rename toyStudy/{ => figs}/fig_scale_with_sigma.png (100%) diff --git a/README.md b/README.md index 6b3e4f6..09c60ba 100644 --- a/README.md +++ b/README.md @@ -169,10 +169,6 @@ Here, `-s` option can be used if only limits for `kt>0` are produced. In this ca plot is simply drawn symmetrically over (0,0) point in (kl,kt) coordinates. -PS. In order to reproduce the _EPS17_ results, follow the instructions here: -[SmartScripts/README.md](SmartScripts/README.md) - - ### Working examples for Resonant case diff --git a/toyStudy/README.md b/toyStudy/README.md index ad72819..00cb005 100644 --- a/toyStudy/README.md +++ b/toyStudy/README.md @@ -1,4 +1,9 @@ -## How to play this toy +## Read the workspaces + +A script called [readWS.py](readWS.py) alows to read the workspaces from the signal and +background of the actual analysis (also commited here) + +## How to play the toys ### Cut and count @@ -9,7 +14,22 @@ The corresponding script is [toyLimit_cut_n_count.py](toyLimit_cut_n_count.py). ``` python toyLimit_cut_n_count.py ``` You will get a plot like this: -![Cut-n-count results](fig_cut_n_count.png) +![Cut-n-count results](figs/fig_cut_n_count.png) + +As we can see the relationship between the limit and &sqrt(N_bkg) is indeed +linear. However, we also notice that the line does not cross zero. That means that there +is an offset in the scaling of the limits. We are at the level of small number of events +in the background. From the backgound `mgg` shape `dN/dmgg = 2 events/GeV`. If we +consider two cases of widths, 2 GeV and 3.2 GeV, we get 4 and 6.4 events +correspondingly. So let's take those numbers and look at how the limits scale: + +| N_sig | Limit with N_bkg=4 events | Limit with N_Bkg=6.4 events| (L(4)-L(6.4))/L(4) | compare to &sqrt;6.4/&sqrt;4 - 1 | +| - | - | - | - | - | +| 2 | 2.71 | 3.23 | 0.193 | 0.265 | +| 4 | 1.36 | 1.62 | 0.193 | 0.265 | +| 6 | 0.90 | 1.08 | 0.199 | 0.265 | + +That is, already with the counting experiment the limit change is smaller than 26%.. ### Play with shapes @@ -19,11 +39,11 @@ will be replacing `%SIG%`, `%BKG%` and `%SW%` within [toyLimit_shape_n_roll.py]( ``` python toyLimit_shape_n_roll.py ``` You will get a plot like this, which shows how the limits scale with the width of the gaussian: -![Shape results](fig_scale_with_sigma.png) +![Shape results](figs/fig_scale_with_sigma.png) And here are the toys generated for that game: -![Toy data](fig_gen_bkg.png) +![Toy data](figs/fig_gen_bkg.png) diff --git a/toyStudy/fig_cut_n_count.png b/toyStudy/fig_cut_n_count.png deleted file mode 100644 index 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toyStudy/fig_gen_bkg.png rename to toyStudy/figs/fig_gen_bkg.png diff --git a/toyStudy/fig_scale_with_sigma.png b/toyStudy/figs/fig_scale_with_sigma.png similarity index 100% rename from toyStudy/fig_scale_with_sigma.png rename to toyStudy/figs/fig_scale_with_sigma.png diff --git a/toyStudy/readWS.py b/toyStudy/readWS.py index b6b5ce6..0f3cb91 100644 --- a/toyStudy/readWS.py +++ b/toyStudy/readWS.py @@ -1,34 +1,118 @@ #! /usr/bin/env python -import os,sys, argparse, time -import tempfile, getpass, subprocess + +#import os,sys import numpy as np import matplotlib.pyplot as plt -username = getpass.getuser() from ROOT import * gROOT.SetBatch() +# -- +# First, let's get the shape of the signal from the analysis workspace +# -- -# Get the shape of the background from a real card -rooWsFile = TFile('hhbbgg.inputbkg_13TeV.root') -anaWs = rooWsFile.Get('w_all') -anaWs.Print() +rooWsSig = TFile('hhbbgg.mH125_13TeV.inputsig.root') +#rooWsSig = TFile('hhbbgg.mH125_13TeV.inputsig_bugged.root') +sigWs = rooWsSig.Get('w_all') +sigWs.Print() -mgg = anaWs.var('mgg') -mgg.Print() +mgg = sigWs.var('mgg') +mjj = sigWs.var('mjj') -anaBkgPdf = anaWs.pdf("mggBkgTmpBer1_cat0_CMS_Bkg_cat2") -fakeData = anaBkgPdf.generate(RooArgSet(mgg), 120) - -anaBkgPdf.Print() + +anaSig_mgg = sigWs.pdf("mggSig_cat0_CMS_sig_cat2") +anaSig_mjj = sigWs.pdf("mjjSig_cat0_CMS_sig_cat2") +anaSig_prod = sigWs.pdf("CMS_sig_cat2") +sigDataSet = sigWs.data("Sig_cat2") + +# Printout the parameters of the PDFs: +l0 = RooArgSet(mgg,mjj) +pars = anaSig_prod.getParameters(l0) +pars.Print() +parsiter = pars.createIterator() +var=parsiter.Next() +while var!=None: + print '%s: %.3f +/ %.3f'%(var.GetName(), var.getVal(), var.getError()) + var=parsiter.Next() + + +# Make some plots: c = TCanvas("c","c",0,0,900,600) c.cd() +mgg.setRange('signal',118,135) +mjj.setRange('signal', 70,190) + +mggFrame = mgg.frame(RooFit.Range("signal")) +sigDataSet.plotOn(mggFrame, RooFit.Binning(80)) +anaSig_mgg.plotOn(mggFrame, RooFit.Name("Sig_mgg"), RooFit.LineColor(kRed+1), RooFit.LineWidth(2)) +mggFrame.Draw() +c.SaveAs('tmpfig_sig_mgg.png') + + +mjjFrame = mjj.frame(RooFit.Range("signal")) +sigDataSet.plotOn(mjjFrame, RooFit.Binning(30)) +anaSig_mjj.plotOn(mjjFrame, RooFit.Name("Sig_mjj"), RooFit.LineColor(kGreen+1), RooFit.LineWidth(2)) +mjjFrame.Draw() +c.SaveAs('tmpfig_sig_mjj.png') + + +# -- +# Now, let's get the shape of the background from the analysis workspace +# -- + +rooWsBkg = TFile('hhbbgg.inputbkg_13TeV.root') +bkgWs = rooWsBkg.Get('w_all') +bkgWs.Print() + +mgg = bkgWs.var('mgg') +mjj = bkgWs.var('mjj') +#mgg.Print() + +anaBkg_mgg = bkgWs.pdf("mggBkgTmpBer1_cat0_CMS_Bkg_cat2") +anaBkg_mjj = bkgWs.pdf("mjjBkgTmpBer1_cat0_CMS_Bkg_cat2") + +realData = bkgWs.data("data_obs_cat2") + +anaBkg_mgg.Print() +anaBkg_mjj.Print() + +print anaBkg_mgg.getVal(), anaBkg_mgg.getNorm() +print anaBkg_mjj.getVal(), anaBkg_mjj.getNorm() + +# Evaluating the PDFs at 125 GeV +N_data = realData.numEntries() +print N_data +mgg.setVal(125) +mjj.setVal(125) + +dNmgg = N_data*anaBkg_mgg.getVal(RooArgSet(mgg))/anaBkg_mgg.getNorm() +dNmjj = N_data*anaBkg_mjj.getVal(RooArgSet(mjj))/anaBkg_mjj.getNorm() + +# Sigma_effectives times 2 +dMgg = 2*1.6 +dMjj = 2*18.3 + +DeltaN = dNmgg*dNmjj*dMgg*dMjj + +print 'Bkg PDF at 125:' +print '\t mgg=', dNmgg, 'mjj=', dNmjj, 'dN/{dm_gg*d_mjj} =', dNmgg*dNmjj +print "DeltaN = ", DeltaN, ", sqrt(DeltaN) =", np.sqrt(DeltaN) + +# Make a plot of backgrounds as well: +fakeData = anaBkg_mgg.generate(RooArgSet(mgg), 120) + +mggFrame = mgg.frame() +realData.plotOn(mggFrame, RooFit.Binning(80), RooFit.Name('data1')) +#fakeData.plotOn(mggFrame, RooFit.Binning(80), RooFit.Name('data1')) +anaBkg_mgg.plotOn(mggFrame, RooFit.Name("Bkg_mgg"), RooFit.LineColor(kBlue), RooFit.LineWidth(2), RooFit.FillColor(kCyan-6)) +mggFrame.Draw() + +#func = mggFrame.findObject("Bkg_mgg") +#print "Eval from func =", func.Eval(125) + +c.SaveAs('tmpfig_bkg.png') + -testFrame = mgg.frame() -fakeData.plotOn(testFrame, RooFit.Binning(80), RooFit.Name('data1')) -anaBkgPdf.plotOn(testFrame, RooFit.Name("Bkg"), RooFit.LineColor(kBlue), RooFit.LineWidth(2), RooFit.FillColor(kCyan-6)) -testFrame.Draw() -c.SaveAs('fig_ana.png') diff --git a/toyStudy/toyLimit_cut_n_count.py b/toyStudy/toyLimit_cut_n_count.py index 76fe81a..9c345e7 100644 --- a/toyStudy/toyLimit_cut_n_count.py +++ b/toyStudy/toyLimit_cut_n_count.py @@ -1,5 +1,5 @@ #! /usr/bin/env python -import os,sys, argparse, time +import os,sys,time import tempfile, getpass, subprocess import numpy as np import matplotlib.pyplot as plt @@ -8,26 +8,33 @@ from ROOT import * gROOT.SetBatch() -Nbkg = np.array([2,2.5,3,3.5,4,4.5,5,6,8,10,15,20,30]) +Nbkg = np.array([2, 4, 6, 6.4, 8, 10, 15, 20, 30, 50]) Nsig = np.array([2, 4, 6]) toyCard1 = 'card_cut_n_count.txt' -processes = [] +import argparse +parser = argparse.ArgumentParser(description='Cut and count toy game') +parser.add_argument('--dry', dest="dry", action="store_true", default=False, + help="Dry run, without running the limits. Assume the output files of combine exist, so just make the plots.") +opt = parser.parse_args() + +processes = [] with open(toyCard1, 'r') as templateCard: tmpCard = templateCard.read() for si in Nsig: for N in Nbkg: with tempfile.NamedTemporaryFile(dir='/tmp/'+username, prefix='toyCard_N'+str(N), suffix='.txt', delete=False) as card: newCard = tmpCard.replace('%BKG%',str(N)).replace('%SIG%',str(si)) - print N + # print N #print newCard card.write(newCard) - print card.name - pro = subprocess.Popen(['combine','-M','Asymptotic', '-m', '125','-n','_CutCount_NBKG_'+str(N)+'_NSIG_'+str(si), card.name]) - processes.append(pro) - time.sleep(0.2) + if not opt.dry: + print card.name + pro = subprocess.Popen(['combine','-M','Asymptotic', '-m', '125','-n','_CutCount_NBKG_'+str(N)+'_NSIG_'+str(si), card.name]) + processes.append(pro) + time.sleep(0.2) # Wait till all processes are finished: for p in processes: @@ -52,18 +59,38 @@ lims.append(tree.GetV1()[2]) rfile.Close() print N, lims[-1] - limsAll[str(si)] = lims + limsAll[str(si)] = np.array(lims) print 'Expected limit at r=0.5: ', lims print limsAll -plt.plot(np.sqrt(Nbkg), limsAll['2'], 'ro', label="Sig = 2 Ev") -plt.plot(np.sqrt(Nbkg), limsAll['4'], 'bs', label="Sig = 4 Ev") -plt.plot(np.sqrt(Nbkg), limsAll['6'], 'g^', label="Sig = 6 Ev") +plt.plot(np.sqrt(Nbkg), limsAll['2'], 'ro', label="N(sig) = 2 ev") +plt.plot(np.sqrt(Nbkg), limsAll['4'], 'bs', label="N(sig) = 4 ev") +plt.plot(np.sqrt(Nbkg), limsAll['6'], 'g^', label="N(sig) = 6 ev") plt.axis([0, 8, 0, 8]) plt.title('Limits from toy counting experiments') plt.xlabel(r'$\sqrt{N_{bkg}}$') plt.ylabel('Median expected Limit') plt.legend() -plt.savefig('fig_cut_n_count.png') +plt.savefig('tmpfig_cut_n_count.png') + +for si in Nsig: + print "Nsig = ", si + # Pick the numbers close to our real analysis + lim_1 = limsAll[str(si)][1] # For Nbkg = 4.0 ev + lim_2 = limsAll[str(si)][3] # For Nbkg = 6.4 ev + + exp_diff = np.sqrt(6.4)/np.sqrt(4) - 1 + diff = (lim_2 - lim_1)/lim_1 + print "| %i | %.2f | %.2f | %.3f | %.3f |" % (si, lim_1, lim_2, diff, exp_diff) + + + # Pick the numbers for large background + lim_1 = limsAll[str(si)][-2] # For Nbkg = 30 ev + lim_2 = limsAll[str(si)][-1] # For Nbkg = 50 ev + + exp_diff = np.sqrt(50)/np.sqrt(30) - 1 + diff = (lim_2 - lim_1)/lim_1 + print "| %i | %.2f | %.2f | %.2f | %.3f |" % (si, lim_1, lim_2, diff, exp_diff) + diff --git a/toyStudy/toyLimit_shape_n_roll.py b/toyStudy/toyLimit_shape_n_roll.py index 25b1cf2..548acfe 100644 --- a/toyStudy/toyLimit_shape_n_roll.py +++ b/toyStudy/toyLimit_shape_n_roll.py @@ -1,5 +1,5 @@ #! /usr/bin/env python -import os,sys, argparse, time +import os,sys,time import tempfile, getpass, subprocess import numpy as np import matplotlib.pyplot as plt @@ -9,6 +9,11 @@ gROOT.SetBatch() +import argparse +parser = argparse.ArgumentParser(description='Shape limits toy game') +parser.add_argument('--dry', dest="dry", action="store_true", default=False, + help="Dry run, without running the limits. Assume the output files of combine exist, so just make the plots.") +opt = parser.parse_args() c = TCanvas("c","c",0,0,900,600) c.cd() @@ -31,7 +36,7 @@ sigPdf.plotOn(testFrame, RooFit.Name("fake sig"), RooFit.LineColor(kRed+2), RooFit.LineWidth(2), RooFit.Normalization(0.10)) testFrame.Draw() -c.SaveAs('fig_gen_bkg.png') +c.SaveAs('tmpfig_gen_bkg.png') w.writeToFile('ws.root') @@ -51,10 +56,11 @@ newCard = tmpCard.replace('%BKG%',str(N)).replace('%SIG%',str(si)).replace('%SW%',str(sw)) card.write(newCard) - print card.name - pro = subprocess.Popen(['combine','-M','Asymptotic', '-m', '125','-n','_Shape_NBKG_'+str(N)+'_NSIG_'+str(si)+'_sw_'+str(sw), card.name]) - processes.append(pro) - time.sleep(0.2) + if not opt.dry: + print card.name + pro = subprocess.Popen(['combine','-M','Asymptotic', '-m', '125','-n','_Shape_NBKG_'+str(N)+'_NSIG_'+str(si)+'_sw_'+str(sw), card.name]) + processes.append(pro) + time.sleep(0.2) # Wait till all processes are finished: @@ -91,10 +97,20 @@ for si in Nsig: for N in Nbkg: plt.plot(np.sqrt(Sigmas), limsAll['NBKG_'+str(N)+'_NSIG_'+str(si)], marker = marker.next(), label='$N_{bkg} = '+str(N)+'; N_{sig} = '+str(si)+'$') -plt.axis([0.5, 2.5, 0, 8]) +plt.axis([0., 2.5, 0, 8]) plt.title('Limits from toy shapes') plt.xlabel(r'$\sqrt{\sigma_{eff}(signal)}}$') plt.ylabel('Median expected Limit') plt.legend() -plt.savefig('fig_scale_with_sigma.png') +plt.savefig('tmpfig_scale_with_sigma.png') + +for si in Nsig: + for N in Nbkg: + print "Nbkg = ", N, 'NSig = ', si + l_1p0 = limsAll['NBKG_'+str(N)+'_NSIG_'+str(si)][2] + l_1p6 = limsAll['NBKG_'+str(N)+'_NSIG_'+str(si)][5] + + print "limits with sigma=1.0 GeV:", l_1p0 + print "limits with sigma=1.6 GeV:", l_1p6 + print "\t diff =", (l_1p6-l_1p0)/l_1p0 From 910cdbd92cd6baee5d33cdc5580676a443b2734c Mon Sep 17 00:00:00 2001 From: Andrey Pozdnyakov Date: Sat, 31 Mar 2018 19:39:03 +0200 Subject: [PATCH 04/12] Adding crystal ball shape in the toy --- toyStudy/README.md | 81 +++++++++++++--- toyStudy/card_shape_n_roll.txt | 10 +- toyStudy/figs/fig_gen_CB_bug.png | Bin 0 -> 14992 bytes toyStudy/figs/fig_gen_CB_fix.png | Bin 0 -> 15052 bytes toyStudy/figs/fig_gen_bkg.png | Bin 14878 -> 14865 bytes toyStudy/figs/fig_scale_with_sigma.png | Bin 47342 -> 59757 bytes toyStudy/hhbbgg.inputbkg_13TeV_bugged.root | Bin 0 -> 29931 bytes toyStudy/hhbbgg.mH125_13TeV.inputsig.root | Bin 0 -> 2911824 bytes .../hhbbgg.mH125_13TeV.inputsig_bugged.root | Bin 0 -> 2598765 bytes toyStudy/readWS.py | 17 ++-- toyStudy/toyLimit_shape_n_roll.py | 89 +++++++++++++----- 11 files changed, 148 insertions(+), 49 deletions(-) create mode 100644 toyStudy/figs/fig_gen_CB_bug.png create mode 100644 toyStudy/figs/fig_gen_CB_fix.png create mode 100644 toyStudy/hhbbgg.inputbkg_13TeV_bugged.root create mode 100644 toyStudy/hhbbgg.mH125_13TeV.inputsig.root create mode 100644 toyStudy/hhbbgg.mH125_13TeV.inputsig_bugged.root diff --git a/toyStudy/README.md b/toyStudy/README.md index 00cb005..1056fb3 100644 --- a/toyStudy/README.md +++ b/toyStudy/README.md @@ -1,6 +1,6 @@ ## Read the workspaces -A script called [readWS.py](readWS.py) alows to read the workspaces from the signal and +A script called [readWS.py](readWS.py) allows to read the workspaces from the signal and background of the actual analysis (also commited here) ## How to play the toys @@ -11,40 +11,97 @@ A template card for this game is [card_cut_n_count.txt](card_cut_n_count.txt), i the strings `%SIG%` and `%BKG%` will be replaced in a script. The corresponding script is [toyLimit_cut_n_count.py](toyLimit_cut_n_count.py). Just run it: -``` python toyLimit_cut_n_count.py ``` +``` +python toyLimit_cut_n_count.py +``` You will get a plot like this: ![Cut-n-count results](figs/fig_cut_n_count.png) -As we can see the relationship between the limit and &sqrt(N_bkg) is indeed +As we can see the relationship between the limit and &Sqrt(N_bkg) is indeed linear. However, we also notice that the line does not cross zero. That means that there is an offset in the scaling of the limits. We are at the level of small number of events in the background. From the backgound `mgg` shape `dN/dmgg = 2 events/GeV`. If we consider two cases of widths, 2 GeV and 3.2 GeV, we get 4 and 6.4 events correspondingly. So let's take those numbers and look at how the limits scale: -| N_sig | Limit with N_bkg=4 events | Limit with N_Bkg=6.4 events| (L(4)-L(6.4))/L(4) | compare to &sqrt;6.4/&sqrt;4 - 1 | +| N_sig | Limit with N_bkg=4 events | Limit with N_Bkg=6.4 events| (L(4)-L(6.4))/L(4) | compare to √6.4/√4 - 1 | | - | - | - | - | - | | 2 | 2.71 | 3.23 | 0.193 | 0.265 | | 4 | 1.36 | 1.62 | 0.193 | 0.265 | | 6 | 0.90 | 1.08 | 0.199 | 0.265 | -That is, already with the counting experiment the limit change is smaller than 26%.. +That is, already with the counting experiment the limit change is smaller than 26%. ### Play with shapes Template card for this game is [card_shape_n_roll.txt](card_shape_n_roll.txt). Here we -will be replacing `%SIG%`, `%BKG%` and `%SW%` within [toyLimit_shape_n_roll.py](toyLimit_shape_n_roll.py) script. +will be replacing `%SIG%`, `%BKG%` and `%SIGMA%` within +[toyLimit_shape_n_roll.py](toyLimit_shape_n_roll.py) script. In the analysis, Nsig = 4 +events, N_bkg = 118 events (total number in 100 < mgg < 180 GeV), sigma = 1.0 (with +a bug) or 1.6 GeV (corrected). Signal shape is Gaussian with mean at 125 GeV and variable +σ, while the background is a simple Exponential function. -``` python toyLimit_shape_n_roll.py ``` -You will get a plot like this, which shows how the limits scale with the width of the gaussian: -![Shape results](figs/fig_scale_with_sigma.png) - - -And here are the toys generated for that game: +The toys generated for that game as well as the background fit used are shown here: ![Toy data](figs/fig_gen_bkg.png) +``` +python toyLimit_shape_n_roll.py +``` + +After running the script, you will get a plot like this, which shows how the limits scale with the width of the gaussian: +![Shape results](figs/fig_scale_with_sigma.png) +Indeed, the scaling is as √σ, nevertheless the ratio at 1.6 to 1.0 GeV sigmas are as follows: + +| N_bkg | N_sig | Limit with σ(sig) = 1 GeV | Limit with σ(sig) = 1.6 GeV| (L(1.0)-L(1.6))/L(1.0) | compare to √1.6/√1 - 1 | +|-|-|-|-|-|-| +| 100 | 2 | 3.10 | 3.70 | 0.194 | 0.265 | +| 120 | 2 | 3.33 | 3.98 | 0.197 | 0.265 | +| 140 | 2 | 3.52 | 4.27 | 0.213 | 0.265 | +| 100 | 4 | 1.55 | 1.85 | 0.194 | 0.265 | +| *120* | *4* | *1.66* | *1.99* | *0.197* | *0.265* | +| 140 | 4 | 1.76 | 2.13 | 0.213 | 0.265 | +| 100 | 6 | 1.04 | 1.24 | 0.196 | 0.265 | +| 120 | 6 | 1.11 | 1.33 | 0.205 | 0.265 | +| 140 | 6 | 1.18 | 1.42 | 0.206 | 0.265 | + +(in bold is the case closest to our analysis) + +Now, let's do a similar thing and instead of using Gasssian for the signal shape we use Double Sided +Crystal Ball functiio with exactly the same parameters as in the analysis workspaces (before and after the bug fix). +Here are the results: + + +![Toy data and CB signal (bugged)](figs/fig_gen_CB_bug.png) +![Toy data and CB signal (fixed)](figs/fig_gen_CB_fix.png) + + +| N_bkg | N_sig | Limit with bug, σ(eff) = 1 GeV | Limit after fix σ(eff) = 1.6 GeV| (L(bug)-L(fix))/L(bug) | compare to √1.6/√1 - 1 | +|-|-|-|-|-|-| +| 100 | 2 | 3.27 | 3.77 | 0.153 | 0.265 | +| 120 | 2 | 3.52 | 4.05 | 0.151 | 0.265 | +| 140 | 2 | 3.73 | 4.33 | 0.159 | 0.265 | +| 100 | 4 | 1.63 | 1.88 | 0.153 | 0.265 | +| *120* | *4* | *1.76* | *2.02* | *0.151* | *0.265* | +| 140 | 4 | 1.87 | 2.16 | 0.159 | 0.265 | +| 100 | 6 | 1.09 | 1.26 | 0.158 | 0.265 | +| 120 | 6 | 1.17 | 1.36 | 0.161 | 0.265 | +| 140 | 6 | 1.24 | 1.44 | 0.164 | 0.265 | + +The 15% difference is what we observe in the analysis as well. + +Note: the width of 1.0 and 1.6 GeV are the _effective sigmas_ of the PDF. In the case of +Crystal Ball PDFs with large tails, a simple scaling with the σ_eff breaks. + + + + + + + + + diff --git a/toyStudy/card_shape_n_roll.txt b/toyStudy/card_shape_n_roll.txt index f5e1de6..01853c8 100644 --- a/toyStudy/card_shape_n_roll.txt +++ b/toyStudy/card_shape_n_roll.txt @@ -2,10 +2,10 @@ imax 1 jmax 1 kmax * --------------- -#shapes * * ws.root w:$PROCESS -shapes sig bin1 ws.root w:sig -shapes bkg bin1 ws.root w:bkg -shapes data_obs bin1 ws.root w:data_obs +shapes * * ws.root w:$PROCESS +#shapes sig bin1 ws.root w:sig +#shapes bkg bin1 ws.root w:bkg +#shapes data_obs bin1 ws.root w:data_obs --------------- bin bin1 observation -1 @@ -19,6 +19,6 @@ rate %SIG% %BKG% lumi lnN 1.03 - sig_sys lnN 1.10 - -sigma param %SW% 0.01 +sigma param %SIGMA% 0.01 nuisance edit freeze sigma diff --git a/toyStudy/figs/fig_gen_CB_bug.png b/toyStudy/figs/fig_gen_CB_bug.png new file mode 100644 index 0000000000000000000000000000000000000000..78e383d0cd9de55c328f6216e728af8e80175a55 GIT 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