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Strength in numbers: optimal and scalable combination of LHC new-physics searches

by Jack Y. Araz, Andy Buckley, Benjamin Fuks, Humberto Reyes-Gonzalez, Wolfgang Waltenberger, Sophie L. Williamson, Jamie Yellen

This is not the latest submitted version.

Submission summary

Authors (as Contributors): Jack Araz · Andy Buckley · Benjamin Fuks · Humberto Reyes-González
Submission information
Arxiv Link: https://arxiv.org/abs/2209.00025v2 (pdf)
Code repository: https://gitlab.com/t-a-c-o/taco_code
Date submitted: 2022-11-23 17:10
Submitted by: Reyes-González, Humberto
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • High-Energy Physics - Experiment
  • High-Energy Physics - Phenomenology

Abstract

To gain a comprehensive view of what the LHC tells us about physics beyond the Standard Model (BSM), it is crucial that different BSM-sensitive analyses can be combined. But in general, search analyses are not statistically orthogonal, so performing comprehensive combinations requires knowledge of the extent to which the same events co-populate multiple analyses' signal regions. We present a novel, stochastic method to determine this degree of overlap and a graph algorithm to efficiently find the combination of signal regions with no mutual overlap that optimises expected upper limits on BSM-model cross-sections. The gain in exclusion power relative to single-analysis limits is demonstrated with models with varying degrees of complexity, ranging from simplified models to a 19-dimensional supersymmetric model.

Current status:
Has been resubmitted



Reports on this Submission

Report 1 by Andrew Fowlie on 2022-11-30 (Invited Report)

Strengths

See first report.

Weaknesses

See first report.

Report

I have spent about 2.5 hours examining the changes and thinking about them. My first report made a number of minor suggestions. I would like to thank the authors for their patience working through my long report. For the most part, I was satisfied by the changes. I didn't see my comment 2.1 (a) addressed though.

My main concern was the lack of clarity over the notion of power used in the paper. This isn't particular to this paper: in my personal opinion, there is a lot of confusion and contradiction over the way 'power' is used in the collider pheno literature, compared to how it would be used (i.e., quite precisely) in a statistical context. The authors address this by adding a comment to the introduction and in the numbered points in sec. 3.2. Unfortunately, I don't think the issue here has been fully resolved. In particular,

i) In the collider literature and in the Asimov approach, we are often making the approximation that Median = expected, and using 'median' and 'expected' interchangeably. In this setting, I agree that the maximum expected significance may be found by maximzing the expected LLR.

ii) But this says nothing about power; it only says something about expected significance. I don't understand the 'power corresponds to ... ' part of the author's response or the 'This [power] is equivalent to maximising ...' part of point 3 in sec. 3.2. Why is maximzing expected significance equivalent to maximizing power?

As I commented in my first report, as far as I can tell, in this setting and under the Wald approximation, the power depends on the expectation of the LLR under the null *and* the alternative model (as well as a choice of fixed T1 error rate). Under each model, the test-statistic q = - 2 LLR follows a normal distribution with a mean and variance related by variance = 4. * |mean|. To find the power, you need to know the distribution of q under each model. Use the distribution under H0 to fix the T1 error. Use the distribution under H1 to compute the power at that fixed T1 error.

Perhaps there are some extra assumptions that the authors are making? The response hints at this (e.g., 'given some fairly reasonable approximations'; what approximations?). On the other hand, since it is common in the literature and since I expect power and expected significance under H1 to be quite closely related, it is reasonable to use it as a proxy, which is particularly useful in this setting since LLR is additive and so we have a sense in which power is additive which is required for the algorithm developed here. I think that would be perfectly reasonable so long as the logic is clarified.

Finally, there are typos in the changes in the text below eq. 3 (',,' and 'through by').

Requested changes

1. Address outsanding item from first report (2.1 (a))
2. Clarify relation between power and expected LLR
3. Fix typos

  • validity: good
  • significance: good
  • originality: good
  • clarity: good
  • formatting: excellent
  • grammar: excellent

Author:  Humberto Reyes-González  on 2022-12-23  [id 3187]

(in reply to Report 1 by Andrew Fowlie on 2022-11-30)

Apologies for the missed point, and what we suspect is a wrong inference on our part about the connection between power and expected significance. We have addressed these points in the latest version, and respond to the review text below.

I didn't see my comment 2.1 (a) addressed though.

The corresponding paragraph has been rephrased.

We used a simplified model approach with the intention of obtaining robust conclusions about potential signal overlaps for arbitrary scenarios. In certain cases, such as simplified model base reinterpretation, the assessment of overlap between two analyses must be generalised for any scenario (within the convex hulls), since such approach doesn’t involve MC event generation and thus overlaps can’t be determined on the fly. Nonetheless, in the case of so-called full (MC-event based) recasting, we can certainly determine the orthogonality between LHC analyses for each specific scenario under consideration. In fact, we did this for Example 3 in the paper.

My main concern was the lack of clarity over the notion of power used in the paper. This isn't particular to this paper: in my personal opinion, there is a lot of confusion and contradiction over the way 'power' is used in the collider pheno literature, compared to how it would be used (i.e., quite precisely) in a statistical context. The authors address this by adding a comment to the introduction and in the numbered points in sec. 3.2. Unfortunately, I don't think the issue here has been fully resolved. In particular,

...

ii) But this says nothing about power; it only says something about expected significance. I don't understand the 'power corresponds to ... ' part of the author's response or the 'This [power] is equivalent to maximising ...' part of point 3 in sec. 3.2. Why is maximizing expected significance equivalent to maximizing power?

As I commented in my first report, as far as I can tell, in this setting and under the Wald approximation, the power depends on the expectation of the LLR under the null and the alternative model (as well as a choice of fixed T1 error rate). Under each model, the test-statistic q = - 2 LLR follows a normal distribution with a mean and variance related by variance = 4. * |mean|. To find the power, you need to know the distribution of q under each model. Use the distribution under H0 to fix the T1 error. Use the distribution under H1 to compute the power at that fixed T1 error.

You are quite right! Our intention was always to maximise the significance, and we had been using the word "power" informally to represent that... and then erroneously concluded that they were interchangeable here (we are not sure why, so thank you for insisting) and we could continue with that nomenclature.

You have clarified that it is indeed inaccurate, and probably confusing for more statistically minded readers, so have replaced the word "power" with "significance" or equivalent through the paper.

Finally, there are typos in the changes in the text below eq. 3 (',,' and 'through by').

Fixed! Thanks again.

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