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star-fcv-l - Re: [Star-fcv-l] Discussion of systematic uncertainty calculation - FCV PWG meeting on 06/December/2023 Wed. 9:30 AM EDT

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  • From: dshen <dshen AT rcf.rhic.bnl.gov>
  • To: "Wang, Fuqiang" <fqwang AT purdue.edu>
  • Cc: "STAR Flow, Chirality and Vorticity PWG" <star-fcv-l AT lists.bnl.gov>
  • Subject: Re: [Star-fcv-l] Discussion of systematic uncertainty calculation - FCV PWG meeting on 06/December/2023 Wed. 9:30 AM EDT
  • Date: Fri, 08 Dec 2023 12:51:00 +0800

Hi Fuqiang,

That's based on experience and common sense, like the choice of DCA<0.1 is against common sense.
There is no way to prove it on fundamental level, I think.

Best,
Diyu

On 2023-12-08 11:32, Wang, Fuqiang wrote:
Hi Diyu,

You say
“We don't have to scan the DCA to find the min and mix number, we just
need to find a reasonable range that we are confident to cover the
non-biased value.”

But how?

Best regards,
Fuqiang

On Dec 7, 2023, at 9:51 PM, dshen <dshen AT rcf.rhic.bnl.gov> wrote:

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Hi Fuqiang,

I disagree with this statement:
"For example, just for the sake of illustration, it is possible that
DCA<1.5 cm gives the min. result and DCA<0.8 cm gives the max result,
however, one would have to scan the DCA space to know this."
We don't have to scan the DCA to find the min and mix number, we just
need to find a reasonable range that we are confident to cover the
non-biased value. Certainly you will have a large variation if you use
DCA<0.01 - there are only few tracks, but we don't use it based on
common sense.

Best,
Diyu


On 2023-12-08 10:30, Wang, Fuqiang wrote:
Hi Diyu,

Please see comments in color below.

Best regards,
Fuqiang

-------------------------

From: dshen <dshen AT rcf.rhic.bnl.gov>
Sent: Thursday, December 7, 2023 7:07 PM
To: STAR Flow, Chirality and Vorticity PWG <star-fcv-l AT lists.bnl.gov>
Cc: Wang, Fuqiang <fqwang AT purdue.edu>
Subject: Re: [Star-fcv-l] Discussion of systematic uncertainty
calculation - FCV PWG meeting on 06/December/2023 Wed. 9:30 AM EDT

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Hi Fuqiang,

It seems we have an agreement on the first point, i.e. the result to
lie
between def - diff and def + diff. It doesn't say the diff should be
the
maximum, say, it has to be default to DCA<0.01 or <100.

Just to make sure we're on the same page: If we say the results lie
between def - diff and def + diff, we mean these are min and max. We
do have to make reasonably sure these are the min-max range. They of
course do not have to come from the min-max range of the cut, as the
result may not linearly depend on the cut. For example, just for the
sake of illustration, it is possible that DCA<1.5 cm gives the min.
result and DCA<0.8 cm gives the max result, however, one would have to
scan the DCA space to know this.

Regarding 1 sigma should be diff/sqrt(12) or 2*diff/sqrt(12), let me
explain it in terms of probability.
Let's take an example, say, the measured quantity is 0, and the
variation is 1. Then we assume the non-biased value is in between -1
to
1 with a uniform distribution. So I present the result as 0 +-
1/sqrt(12), it means the non-biased value falls within +- 1/sqrt(12)
with a probability of 2*1/sqrt(12) which is exactly the standard
deviation of 2*varition=2. If you define 1 sigma as
2*variation/sqrt(12), then we should present as +- half sigma to have
the same probability as before.

For a flat distribution of width 2, the equivalent Gaussian sigma is
2/sqrt(12). So the error is +/- 2/sqrt(12). It is +/- 1/sqrt(3) or
approximately +/- 0.6, or 1.2 out of 2, i.e. 60%.

Thanks,
Diyu

On 2023-12-08 02:17, Wang, Fuqiang via Star-fcv-l wrote:
Hi Diyu,

So the central issue is whether you get the maximum variation. If
one
varies towards only one side, and quote +/- assuming the variation
is
symmetric, then you’re really assuming the result to lie between
min
def-diff and max diff+diff, so you should quote def +/-
diff/sqrt(3).

Best regards,
Fuqiang

On Dec 7, 2023, at 1:08 PM, Wang, Fuqiang <fqwang AT purdue.edu>
wrote:

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Hi Diyu,

I realize that there may be a misunderstanding on the term “max.
variation”. It means variations in cuts that result in maximum
variation in result.

Regarding sqrt(12) vs sqrt(3):
If one believes def. is min and sys. is max, then it’s probably
better
to quote the average of def. and sys. as the central value and +/-
diff/sqrt(12) as the error.
If there’s strong reason to quote the value to be the min. (or
max.
for that matter) and the negative side error is really zero, then
we
should quote the value as def.+diff/sqrt(3) not sqrt(12) because
the
common understanding of error is that it covers 68% probability.

Best regards,
Fuqiang

On Dec 7, 2023, at 10:50 AM, dshen <dshen AT rcf.rhic.bnl.gov>
wrote:

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Hi Fuqiang,

One sigma is |def.-sys.|/sqrt(12), and it shows as +- 1 sigma for
the
case of (def. - |def.-sys.|, def. + |def.-sys.|).
The critical point is that it doesn't require a maximum variation,
it
just requires that the variation could cover the true value. The
confidence level is based on experience and common sense, there is
no
mathematical way to quantify it - it is not statistics.

Best,
Diyu


On 2023-12-07 23:28, Wang, Fuqiang wrote:
Hi Diyu,

What you wrote is just another way to say that the physics
quantity
in
question is within the min and max of (def. - |def.-sys.|, def.
+
|def.-sys.|), respectively. In such a case, one would quote a
sigma
of
2*|def.-sys.|/sqrt(12) = |def.-sys.|/sqrt(3). The essential point
is
to demonstrate to reasonable confidence that this is indeed the
maximum syst. variation in the result.

Best regards,
Fuqiang

On Dec 7, 2023, at 6:32 AM, dshen via Star-fcv-l
<star-fcv-l AT lists.bnl.gov> wrote:

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Hi Fuqiang, Zhiwan and all,

It was a inspiring discussion on the systematic uncertainty
calculations
yesterday, it pushes me to think.
I tend to agree with Zhiwan and what the blind-analysis did,
i.e.
use
denominator of 1/sqrt(12).
The argument was that one shouldn't divide the variation by
1/sqrt(12)
because the variation isn't proved to be the maximum - minimum,
I
think
there is a misunderstanding of the reason behind it.
It isn't based on the assumption that the variation is maximum -
minimum, the underlying assumption is that the true value falls
within
"default cut" +- "variation".
Let's take an example, say, the default cut is DCA<2, and the
systematic
cut is DCA<1.
The assumption is that the non-biased value is in the interval
of
(def.
- |def.-sys.|, def. + |def.-sys.|), and it can be any value in
that
interval with equal probability (uniform distribution) assuming
we
don't
have any pre-knowledge to the best position. That's the reason
of
why
people assign |def.-sys.|/sqrt(12) as 1 sigma and use two-side
band.
It hasn't to be the maximum - minimum, although it isn't
incorrect
technically to use larger uncertainty, say, use Dca<0.1 to
Dca<100.
But
I think the principal is to provide the best estimate instead of
the
most conservative value.
What variation can be considered as reasonable? I think it is
based
on
experience and common sense to a specific physics topic. For CME
study,
like what Zhiwan did, it is reasonable to assume the non-biased
value
falls with in DCA<2 +- |DCA<2 - DCA<1|, for example.

That's my two cents.

Best,
Diyu



On 2023-12-06 05:10, Zhiwan Xu via Star-fcv-l wrote:
Dear Conveners,
I would like to update the paper proposal on the CME search in
STAR
BES-II.
Please kindly add me to the schedule.

The paper proposal webpage:


https://drupal.star.bnl.gov/STAR/blog/zhiwanxu/Paper-Proposal-Search-Chiral-Magnetic-Effect-RHIC-Beam-Energy-Scan-II
[3]
The slides:


https://drupal.star.bnl.gov/STAR/system/files/paper_proposal_CME_BESII_v2.pdf
[4]

Best,
Zhiwan

------------------------------------
Zhiwan Xu,
Department of Physics and Astronomy, UCLA
zhiwanxu AT physics.ucla.edu

----- Original Message -----
From: "subhash via Star-fcv-l" <star-fcv-l AT lists.bnl.gov>
To: "STAR Flow, Chirality and Vorticity PWG"
<star-fcv-l AT lists.bnl.gov>
Cc: "subhash" <subhash AT rcf.rhic.bnl.gov>
Sent: Sunday, December 3, 2023 11:21:34 PM
Subject: [Star-fcv-l] FCV PWG meeting on 06/December/2023 Wed.
9:30
AM
EDT

Dear All,

We shall have our weekly FCV PWG meeting this Wednesday
(06/Dec/2023)
at
9:30 AM EDT. If you would like to present please let us know.
Please
try
posting your slides by Tuesday. The agenda will be collected
at:

https://drupal.star.bnl.gov/STAR/blog/jjiastar/bulkcorr
[5]

Zoom details are copied below.

Thanks and regards,
Prithwish, Zhenyu and Subhash


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