Calculating <i>p</i>-values and their significances with the Energy Test for large datasets

Barter, W.; Burr, C.; Parkes, C.

doi:10.1088/1748-0221/13/04/p04011

Cited by 4 publications

(22 citation statements)

References 9 publications

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“…In this context, φ l are the eigenfunctions, andψ(e i , e j ) = ψ(e i , e j ) − E e ψ(e i , e) − E e,e ψ(e, e ). 4 Not only does this confirm the conjecture of [BBP18], as does [Zec18], it goes further by providing an expression for the limiting distribution for arbitrary kernel function. This distributionp, sometimes referred to as the 'empirical distribution for p', places probability only at the locations where events have already been seen.…”

Section: Related Worksupporting

confidence: 62%

“…Summarising crudely: if p is very similar top then T is expected to take values close to or below zero, while increasing differences between p andp should (at fixed n andn) lead to ever greater positive values for T . The definition of T used in [BBP18] is given in equation (1), T = 1 2 1 n(n − 1) n i =j ψ(e i , e j ) + 1 2 1 n(n − 1)n i =j…”

Section: The T -Statisticmentioning

confidence: 99%

“…to calculate 5-sigma or 15-sigma p-values), independently of whether the T -statistic (or an approximation to it) is costly to calculate. Our work is thus complementary to that of [BBP18]. Future users may apply both strategies at once, or use either separately, depending on their needs.…”

Section: The T -Statisticmentioning

confidence: 99%

“…In passing, we note that users who need to address P1 (perhaps because they have large n), but who cannot use the method of [BBP18] (perhaps because their n is not large enough to make 2 Given the decision to fix δ at 1 2 , there is strong motivation to use distributions p andp having length scales of similar or slightly larger order. For this reason our results in Section 7 use a p which distributes events e i uniformly within a unit cube.…”

Section: The T -Statisticmentioning

confidence: 99%

“…While bootstrap sampling provides nothing more than an estimate of any of the desired properties of T (p, n,n), the literature [Efr81] suggests that differences between estimates and underlying parameters become negligible for our purposes when the number of event min [n,n, m] exceeds 50 or 100. For the purposes of this paper we therefore make the assumption (in keeping with [BBP18]) that bootstrap sampling (rather than 'true' sampling) introduces only negligible uncertainties in all the places we use it. While it is legitimate to question the validity of this assumption, doing so is not relevant for the purposes of comparing our approach to that of [BBP18].…”

Section: Bootstrap Samplingmentioning

confidence: 99%

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Biased bootstrap sampling for efficient two-sample testing

Gillam¹,

Lester

2018

J. Inst.

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The so-called 'energy test' is a frequentist technique used in experimental particle physics to decide whether two samples are drawn from the same distribution. Its usage requires a good understanding of the distribution of the test statistic, T , under the null hypothesis. We propose a technique which allows the extreme tails of the T -distribution to be determined more efficiently than possible with present methods. This allows quick evaluation of (for example) 5-sigma confidence intervals that otherwise would have required prohibitively costly computation times or approximations to have been made. Furthermore, we comment on other ways that T computations could be sped up using established results from the statistics community. Beyond two-sample testing, the proposed biased bootstrap method may provide benefit anywhere extreme values are currently obtained with bootstrap sampling. * GAM Systematic | Cantab † University of Cambridge 1 In brief, the Markov chain history is used to generate an estimator for the underlying Markov chain transition matrix, which is itself used to derive the covariance matrix for every pair of bin counts prior to the weighting and normalisation step. The final uncertainties (after the re-weighting and normalisation process, which introduces further correlations between bins) may then be written as a simple function of the former set of covariances provided that (as has already been assumed) the Markov chain has circulated through most of its domain 'a few' times.

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Section: Related Worksupporting

confidence: 62%

Section: The T -Statisticmentioning

confidence: 99%

Section: The T -Statisticmentioning

confidence: 99%

Section: The T -Statisticmentioning

confidence: 99%

Section: Bootstrap Samplingmentioning

confidence: 99%

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Biased bootstrap sampling for efficient two-sample testing

Gillam¹,

Lester

2018

J. Inst.

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Search for CP violation in the phase space of $$ {D}^0\to {K}_S^0{K}^{\pm }{\pi}^{\mp } $$ decays with the energy test

Aaij,

Abdelmotteleb,

Abellan Beteta

et al. 2024

J. High Energ. Phys.

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A search for CP violation in $$ {D}^0\to {K}_S^0{K}^{+}{\pi}^{-} $$ D 0 → K S 0 K + π − and $$ {D}^0\to {K}_S^0{K}^{-}{\pi}^{+} $$ D 0 → K S 0 K − π + decays is reported. The search is performed using an unbinned model-independent method known as the energy test that probes local CP violation in the phase space of the decays. The data analysed correspond to an integrated luminosity of 5.4 fb−1 collected in proton-proton collisions by the LHCb experiment at a centre-of-mass energy of $$ \sqrt{s} $$ s = 13 TeV, amounting to approximately 950 thousand and 620 thousand signal candidates for the $$ {D}^0\to {K}_S^0{K}^{-}{\pi}^{+} $$ D 0 → K S 0 K − π + and $$ {D}^0\to {K}_S^0{K}^{+}{\pi}^{-} $$ D 0 → K S 0 K + π − modes, respectively. The method is validated using D0 → K−π+π−π+ and $$ {D}^0\to {K}_S^0{\pi}^{+}{\pi}^{-} $$ D 0 → K S 0 π + π − decays, where CP-violating effects are expected to be negligible, and using background-enhanced regions of the signal decays. The results are consistent with CP symmetry in both the $$ {D}^0\to {K}_S^0{K}^{-}{\pi}^{+} $$ D 0 → K S 0 K − π + and the $$ {D}^0\to {K}_S^0{K}^{+}{\pi}^{-} $$ D 0 → K S 0 K + π − decays, with p-values for the hypothesis of no CP violation of 70% and 66%, respectively.

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Search for CP violation in the phase space of D0 → π−π+π0 decays with the energy test

Aaij,

Abdelmotteleb,

Abellan Beteta

et al. 2023

J. High Energ. Phys.

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A search for CP violation in D0 → π−π+π0 decays is reported, using pp collision data collected by the LHCb experiment from 2015 to 2018 corresponding to an integrated luminosity of 6 fb−1. An unbinned model-independent approach provides sensitivity to local CP violation within the two-dimensional phase space of the decay. The method is validated using the Cabibbo-favoured channel D0 → K−π+π0 and background regions of the signal mode. The results are consistent with CP symmetry in this decay.

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Calculating p-values and their significances with the Energy Test for large datasets

Cited by 4 publications

References 9 publications

Biased bootstrap sampling for efficient two-sample testing

Biased bootstrap sampling for efficient two-sample testing

Search for CP violation in the phase space of $$ {D}^0\to {K}_S^0{K}^{\pm }{\pi}^{\mp } $$ decays with the energy test

Search for CP violation in the phase space of D0 → π−π+π0 decays with the energy test

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