STAR Flow, Chirality and Vorticity PWG

["Tang, Aihong" <aihong AT bnl.gov>]

Hi, all :

I wanted to share my perspective on the issue of handling systematic errors to ensure clarity and understanding.

To start, let me walk through the way we usually derive our systematic errors. For an individual systematic source, we operate under the assumption that the underlying distribution is uniform - a reasonable assumption in our context. The RMS of a uniform distribution is well-defined, it is span/sqrt(12). Extending this to multiple independent systematic sources, the final measurement is expected to follow a Gaussian distribution, leading to the total systematic error being the quadrature sum of individual systematic errors.

Let's take the DCA cut as an example of individual systematic error. Say, the default cut is 2cm, with a 1cm variation.  We treat measurements within the range [1,2] cm as equally valid, regardless of the specific cut value. Without more information, this is the most unbiased treatment. Consequently, these measurements are assigned the same systematic uncertainty, reflecting the inability of our experimental setup to differentiate their importance or discern their systematic uncertainties. 

It's essential to recognize that the range of the uniform distribution is an estimation derived from the two boundaries measured with DCA < 2cm and DCA < 1cm, respectively. While usually referred to as maximum and minimum, they are not necessarily the true caps of the actual values but serve as practical estimates. If our statistics allows, we may scan around the [1,2] cm region for verification, but this is typically unpractical when statistical error dominates.   

In some instances, the central (mean) value of the uniform distribution may not align with the default value, which could be on one edge. Despite this, all measurements share the same systematic uncertainty, making it applicable to the default value. We opt for the default of DCA < 2cm due to its minimal statistical error while maintaining validity comparable to the central value or any other value within the uniform distribution. When we have multiple systematic sources, their central values fall on both sides of the default, making the final central value closer to the default.

I have heard the suggestion of adopting a one-way systematic error when the default is at the edge, and I am not sure if it is a good idea. The default value being at the edge doesn't definitely imply that a more appropriate value couldn't exist beyond that edge. In reality, the optimal value might fall outside that range, and assigning a one-way error could incorrectly imply the knowledge on the certainty about the optimal value.

At this level, we are constrained by the ultimate limitation of our experimental device, and we find ourselves relying heavily on assumptions, acknowledging that no procedure is perfect. However, in my perspective, the rationale behind span/sqrt(12) is clear and justifiable. I see no compelling reason to open another extensive discussion on how STAR handles systematic error, in particular in light of the difficult debate we experienced during the writing of the isobar blind analysis paper.

Thanks,

Aihong

On Dec 8, 2023, at 12:03 AM, Huan Zhong Huang via Star-fcv-l <star-fcv-l AT lists.bnl.gov> wrote:

Hi Diyu, All,
 I had a discussion with Zhiwan and I understand that this issue was hotly debated during her paper proposal presentation to the PWG as well. The systematic error estimate is clearly an experimental art, and all the approaches/proposals under discussion are with some merits and disadvantages when viewed from certain perspectives. Zhiwan and I are convinced that the approach in the published isobar CME paper is a well balanced approach approved by the collaboration and we intend to follow in our paper. 
 If people really think that the previous STAR approach in the isobar CME is wrong and intend to push for an erratum to be published by the STAR collaboration to correct the "mistake" soon, we will be happy to take the new approved STAR approach for systematic error estimate. Until then, please do not waste your time and everyone else time to go back and forth on this issue. I have seen enough email exchanges on this topic. If it is not going to converge under normal discussion, then let the STAR publication procedure to take its course.
 I did not mean to start new discussion and do not expect me to respond to emails on this topic. Thanks. Regards,
 Huan

-----Original Message-----
From: Star-fcv-l <star-fcv-l-bounces AT lists.bnl.gov> On Behalf Of dshen via Star-fcv-l
Sent: Thursday, December 7, 2023 6:51 PM
To: Wang, Fuqiang <fqwang AT purdue.edu>
Cc: dshen <dshen AT rcf.rhic.bnl.gov>; 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

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:

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[3]

The slides:

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[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:

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[5]

Zoom details are copied below.

Thanks and regards,
Prithwish, Zhenyu and Subhash


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[4] 
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[5] https://drupal.star.bnl.gov/STAR/blog/jjiastar/bulkcorr
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