Hi Again,

Another way to think about it is to fit a Gaussian to the 24 data points, and analyse whether one of them is an outlier or not. This is analytic given a Gaussian distribution with one outlier and reduces to the Chebychev inequality (or at least, I thought it did).

Thanks,
 
Rob
 
------------------------------------------
Robert Lambert
FOM-VU-NIKHEF-Bfys LHCb
Email: rob.lambert@cern.ch
------------------------------------------
Nikhef N251
Tel: +31 20 592 2131  
Fax: +31 20 592 5155 
------------------------------------------
CERN, 13-1-018 
Tel: +41 22 767 4024 
Fax: +41 22 766 8109
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From: bfys-physics-bounces@nikhef.nl [bfys-physics-bounces@nikhef.nl] on behalf of Rob Lambert [Rob.Lambert@cern.ch]
Sent: 02 July 2013 11:30
To: Diego Martinez Santos; Marcel Merk
Cc: bfys-physics@nikhef.nl
Subject: Re: [Bfys-physics] B->K*mumu paper

(24*0.0001*2)
           ^ missed a zero ....
 
Rob
 
------------------------------------------
Robert Lambert
FOM-VU-NIKHEF-Bfys LHCb
Email: rob.lambert@cern.ch
------------------------------------------
Nikhef N251
Tel: +31 20 592 2131  
Fax: +31 20 592 5155 
------------------------------------------
CERN, 13-1-018 
Tel: +41 22 767 4024 
Fax: +41 22 766 8109
------------------------------------------
From: Rob Lambert
Sent: 02 July 2013 11:29
To: Diego Martinez Santos; Marcel Merk
Cc: bfys-physics@nikhef.nl
Subject: RE: [Bfys-physics] B->K*mumu paper

Hi Diego,

Well, I'm 100% sure that's right because it's just 24*0.001*2, which is the integrated probability for a two-sided Gaussian test, but the question isn't "what's the probability of that happening" which is actually "1", because it did actually happen, but "how many such deviations would you need to see before you can invalidate the null hypothesis of no deviation", and this number is given by Chebychev's equality... well, I thought it was, anyway.

Thanks,
 
Rob
 
------------------------------------------
Robert Lambert
FOM-VU-NIKHEF-Bfys LHCb
Email: rob.lambert@cern.ch
------------------------------------------
Nikhef N251
Tel: +31 20 592 2131  
Fax: +31 20 592 5155 
------------------------------------------
CERN, 13-1-018 
Tel: +41 22 767 4024 
Fax: +41 22 766 8109
------------------------------------------
From: Diego Martinez Santos
Sent: 02 July 2013 11:17
To: Rob Lambert; Marcel Merk
Cc: bfys-physics@nikhef.nl
Subject: RE: [Bfys-physics] B->K*mumu paper

(PS: 0.566 \pm 0.033. forgot the % of course)

Dende: Diego Martinez Santos
Enviado: martes, 02 de xullo de 2013 11:16
Ata: Rob Lambert; Marcel Merk
Cc: bfys-physics@nikhef.nl
Asunto: RE: [Bfys-physics] B->K*mumu paper

Hi

 

I;ve just made quick toyMC, I get that the probability(maxSigma) > 3.7 for experiments consisting

of 24 measurements is 0.566 \pm 0.033.

 

 

Voila the code (needs SetupUrania):

 

from scipy import random as rnd
from Urania import *
AccessPackage("Bs2MuMu")

from RTuple import *

 

def do_set_of_experiments(N):
    l = []
    for i in range(N):
        l.append(abs(rnd.normal()))
    l.sort()
    l.reverse()
    return l[0]

def do_test(N, Nexp = 50000):
    tup = RTuple("File_test",["maxSigma/F"])
    for i in range(Nexp):
        tup.fillItem("maxSigma",do_set_of_experiments(24))
        tup.fill()
    tup.close()

                

 

Then you just call do_test(24) and analyse the produced Ntuple.

 

 

 

Cheers;

 

Diego

 

 

 

 

Dende: bfys-physics-bounces@nikhef.nl [bfys-physics-bounces@nikhef.nl] en nome de Rob Lambert [Rob.Lambert@cern.ch]
Enviado: martes, 02 de xullo de 2013 10:53
Ata: Marcel Merk
Cc: bfys-physics@nikhef.nl
Asunto: Re: [Bfys-physics] B->K*mumu paper

Yes. Chebychev's inequality gives an estimate for how often a deviation this large this should happen, and it seems to be perfectly within the realms of probability, in fact it seems to be expected, and even two such deviations would not be strange.

Gerhard might want to correct me here, though...

Cheers,
 
Rob
 
------------------------------------------
Robert Lambert
FOM-VU-NIKHEF-Bfys LHCb
Email: rob.lambert@cern.ch
------------------------------------------
Nikhef N251
Tel: +31 20 592 2131  
Fax: +31 20 592 5155 
------------------------------------------
CERN, 13-1-018 
Tel: +41 22 767 4024 
Fax: +41 22 766 8109
------------------------------------------
From: Marcel Merk [marcel.merk@nikhef.nl]
Sent: 02 July 2013 10:51
To: Rob Lambert
Cc: bfys-physics@nikhef.nl
Subject: Re: [Bfys-physics] B->K*mumu paper

Hi Rob,
Let me just clarify: you question the claim of 0.5%, is that correct?
just to make sure I understand which point you comment on.
cheers,
- Marcel


On 2 July 2013 10:06, Rob Lambert <Rob.Lambert@cern.ch> wrote:
Erm, just some statistical queries.. what about chebychev's inequality:

http://en.wikipedia.org/wiki/Chebyshev's_inequality

"No more than 1/k^{2} of the distribution's values can be more than k standard deviations away from the mean" 

In this case it is 1/(3.7*3.7) which is 7%, and 24*7% is 1.75, so no more than 1.75 of the observables should be this far away. One deviation this large is perfectly expected from Chebychev's inequality.

Thanks,
 
Rob
 
------------------------------------------
Robert Lambert
FOM-VU-NIKHEF-Bfys LHCb
Email: rob.lambert@cern.ch
------------------------------------------
Nikhef N251
Tel: +31 20 592 2131  
Fax: +31 20 592 5155 
------------------------------------------
CERN, 13-1-018 
 ------------------------------------------
From: bfys-physics-bounces@nikhef.nl [bfys-physics-bounces@nikhef.nl] on behalf of Marcel Merk [marcel.merk@nikhef.nl]
Sent: 01 July 2013 18:01
To: bfys-physics@nikhef.nl
Subject: [Bfys-physics] B->K*mumu paper

Dear bfys-physics friend,
This is to let you know that I collect comments to the paper below.
To stimulate you to read it: we claim that the probability that the measurement is consistent with the Standard Model is only 0.5%. A local discrepancy of 3.7 sigma is observed.

  LHCb PAPER-2013-037:
      "Measurement of form factor independent observables
       in the decay $B^0\to K^{*0}\mu^+\mu^-$"
      Link            : https://cds.cern.ch/record/1557918
      Deadline        : 09-Jul-2013

best regards,
- Marcel

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