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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Fast estimation of the look-elsewhere effect using Gaussian random fields

Abstract We discuss the use of Gaussian random fields to estimate the look-elsewhere effect correction. We show that Gaussian random fields can be used to model the null-hypothesis significance maps from a large set of statistical problems commonly encountered in physics, such as template matching and likelihood ratio tests. Some specific examples are searches for dark matter using pixel arrays, searches for astronomical transients, and searches for fast-radio bursts. Gaussian random fields can be sampled efficiently in the frequency domain, and the excursion probability can be fitted with these samples to extend any estimation of the look-elsewhere effect to lower p values. In addition, in cases where the Gaussian random field is stationary and the parameter space is Euclidean, the look-elsewhere effect correction can be computed analytically. We demonstrate these methods using two example template matching problems. Finally, we apply these methods to estimate the trial factor of a $$4^3$$ 4 3 accelerometer array for the detection of dark matter tracks in the Windchime project. When a global significance of $$3\sigma $$ 3 σ is required, the estimated trial factor for such an accelerometer array is $$10^{14}$$ 10 14 for a one-second search, and $$10^{22}$$ 10 22 for a 1-year search.

Qin, Juehang (ORCID:0000000182288949)↗
DOE OSTI2020

The look-elsewhere effect from a unified Bayesian and frequentist perspective

When searching over a large parameter space for anomalies such as events, peaks, objects, or particles, there is a large probability that spurious signals with seemingly high signi ficance will be found. This is known as the look-elsewhere effect and is prevalent throughout cosmology, (astro)particle physics, and beyond. To avoid making false claims of detection, one must account for this effect when assigning the statistical significance of an anomaly. This is typically accomplished by considering the trials factor, which is generally computed numerically via potentially expensive simulations. In this paper we develop a continuous generalization of the Bonferroni and Sidak corrections by applying the Laplace approximation to evaluate the Bayes factor, and in turn relating the trials factor to the prior-to-posterior volume ratio. Here, we use this to define a test statistic whose frequentist properties have a simple interpretation in terms of the global p-value, or statistical significance. We apply this method to various physics-based examples and show it to work well for the full range of p-values, i.e. in both the asymptotic and non-asymptotic regimes. We also show that this method naturally accounts for other model complexities such as additional degrees of freedom, generalizing Wilks' theorem. This provides a fast way to quantify statistical significance in light of the look-elsewhere effect, without resorting to expensive simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Self-calibrating the look-elsewhere effect: fast evaluation of the statistical significance using peak heights

In experiments where one searches a large parameter space for an anomaly, one often finds many spurious noise-induced peaks in the likelihood. This is known as the look-elsewhere effect, and must be corrected for when performing statistical analysis. Here, this paper introduces a method to calibrate the false alarm probability (FAP), or p-value, for a given dataset by considering the heights of the highest peaks in the likelihood. Specifically, we derive an equation relating the global p-value to the rank and height of local maxima. In the simplest form of self-calibration, the look-elsewhere-corrected $\chi^2$ of a physical peak is approximated by the $\chi^2$ of the peak minus the $\chi^2$ of the highest noise-induced peak, with accuracy improved by considering lower peaks. In contrast to alternative methods, this approach has negligible computational cost as peaks in the likelihood are a byproduct of every peak-search analysis. We apply to examples from astronomy, including planet detection, periodograms, and cosmology.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Unaccounted-for look-elsewhere effect in k-fold cross adaptive anomaly searches

Recently a technique based on k-fold cross validation has become popular in anomaly detection in HEP, as a way to search for a wide class of anomalies in the data, without paying an associated penalty in sensitivity-depth. In this work, we point out that the breadth-depth tradeoff is an unavoidable aspect of anomaly detection, and cannot be overcome using the aforementioned k-fold cross adaptive search technique. Furthermore, we show that the technique leads to unaccounted-for look elsewhere effect, i.e., the underestimation of p-values or the overestimation of significances of observed anomalies.

Shyamsundar, Prasanth [Fermilab]↗
DOE OSTI2022

Statistical Significance Testing for Mixed Priors: A Combined Bayesian and Frequentist Analysis

In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it incorporates Occam’s razor via the multiplicity or trials factor in the look-elsewhere effect. However, if the prior is not known completely, the frequentist hypothesis test via the false-positive rate is a better approach, as it is less sensitive to the prior choice. We argue that when only partial prior information is available, it is best to combine the two methodologies by using the Bayes factor as a test statistic in the frequentist analysis. We show that the standard frequentist maximum likelihood-ratio test statistic corresponds to the Bayes factor with a non-informative Jeffrey’s prior. We also show that mixed priors increase the statistical power in frequentist analyses over the maximum likelihood test statistic. We develop an analytic formalism that does not require expensive simulations and generalize Wilks’ theorem beyond its usual regime of validity. In specific limits, the formalism reproduces existing expressions, such as the p-value of linear models and periodograms. We apply the formalism to an example of exoplanet transits, where multiplicity can be more than 10 7 . We show that our analytic expressions reproduce the $p$-values derived from numerical simulations. We offer an interpretation of our formalism based on the statistical mechanics. We introduce the counting of states in a continuous parameter space using the uncertainty volume as the quantum of the state. We show that both the $p$-value and Bayes factor can be expressed as an energy versus entropy competition.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A strategy for a general search for new phenomena using data-derived signal regions and its application within the ATLAS experiment

This paper describes a strategy for a general search used by the ATLAS Collaboration to find potential indications of new physics. Events are classified according to their final state into many event classes. For each event class an automated search algorithm tests whether the data are compatible with the Monte Carlo simulated expectation in several distributions sensitive to the effects of new physics. The significance of a deviation is quantified using pseudo-experiments. A data selection with a significant deviation defines a signal region for a dedicated follow-up analysis with an improved background expectation. The analysis of the data-derived signal regions on a new dataset allows a statistical interpretation without the large look-elsewhere effect. The sensitivity of the approach is discussed using Standard Model processes and benchmark signals of new physics. As an example, results are shown for 3.2 fb –1 of proton–proton collision data at a centre-of-mass energy of 13 TeV collected with the ATLAS detector at the LHC in 2015, in which more than 700 event classes and more than 10 5 regions have been analysed. Furthermore, no significant deviations are found and consequently no data-derived signal regions for a follow-up analysis have been defined.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Search for the doubly charmed baryon $ {\varXi}_{cc}^{+} $ in the $ {\varXi}_c^{+}{\pi}^{-}{\pi}^{+} $ final state

A search for the doubly charmed baryon $ {\varXi}_{cc}^{+} $ is performed in the $ {\varXi}_c^{+}{\pi}^{-}{\pi}^{+} $ invariant-mass spectrum, where the $ {\varXi}_c^{+} $ baryon is reconstructed in the pK - π + final state. The study uses proton-proton collision data collected with the LHCb detector at a centre- of-mass energy of 13 TeV, corresponding to a total integrated luminosity of 5.4 fb -1 . No significant signal is observed in the invariant-mass range of 3.4–3.8 GeV/ c 2 . Upper limits are set on the ratio of branching fractions multiplied by the production cross-section with respect to the $ {\varXi}_{cc}^{++} $ →( $ {\varXi}_c^{+} $ → pK - π + ) π + decay for different $ {\varXi}_{cc}^{+} $ mass and lifetime hypotheses in the rapidity range from 2.0 to 4.5 and the transverse momentum range from 2.5 to 25 GeV/ c . The results from this search are combined with a previously published search for the $ {\varXi}_{cc}^{+} $ → $ {\varLambda}_c^{+} $ K - π + decay mode, yielding a maximum local significance of 4.0 standard deviations around the mass of 3620 MeV/ c 2 , including systematic uncertainties. Taking into account the look-elsewhere effect in the 3.5–3.7 GeV/ c 2 mass window, the combined global significance is 2.9 standard deviations including systematic uncertainties.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Testing claims of the GW170817 binary neutron star inspiral affecting β-decay rates

On August 17, 2017, the first gravitational wave signal from a binary neutron star inspiral (GW170817) was detected by Advanced LIGO and Advanced VIRGO. Here we present radioactive β-decay rates of three independent sources 44 Ti, 60 Co and 137 Cs, monitored during the same period by a precision experiment designed to investigate the decay of long-lived radioactive sources. We do not find any significant correlations between decay rates in a 5 h time interval following the GW170817 observation. This contradicts a previous claim published in this journal of an observed 2.5σ Pearson Correlation between fluctuations in the number of observed decays from two β-decaying isotopes ( 32 Si and 36 Cl) in the same time interval. By correcting for the choice of an arbitrary time interval, we find no evidence of a correlation above 1.5σ confidence. In addition, we argue that such analyses on correlations in arbitrary time intervals should always correct for the so-called Look-Elsewhere effect by quoting the global significance.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Delving into the depths of NGC 3783 with XRISM

The 2024 X-ray/UV observation campaign of NGC 3783, led by XRISM, revealed the launch of an ultrafast outflow (UFO) with a radial velocity of 0.19c (57 000 km s −1 ). This event is synchronized with the sharp decay, within less than half a day, of a prominent soft X-ray/UV flare. Accounting for the look-elsewhere effect, the XRISM Resolve data alone indicate a low probability of 2 × 10 −5 that this UFO detection is due to random chance. The UFO features narrow H-like and He-like Fe lines with a velocity dispersion of ∼1000 km s −1 , suggesting that it originates from a dense clump. Beyond this primary detection, there are hints of weaker outflow signatures throughout the rise and fall phases of the soft flare. Their velocities increase from 0.05c to 0.3c over approximately three days, and they may be associated with a larger stream in which the clump is embedded. The radiation pressure is insufficient to drive the acceleration of this rapidly evolving outflow. The observed evolution of the outflow kinematics instead closely resembles that of solar coronal mass ejections, implying magnetic driving and, conceivably, reconnection near the accretion disk as the likely mechanisms behind both the UFO launch and the associated soft flare.

Astronomy and AstroPhysics↗
DOE OSTI2012

Fermi LAT search for internal bremsstrahlung signatures from dark matter annihilation

A commonly encountered obstacle in indirect searches for galactic dark matter is how to disentangle possible signals from astrophysical backgrounds. Given that such signals are most likely subdominant, the search for pronounced spectral features plays a key role for indirect detection experiments; monochromatic gamma-ray lines or similar features related to internal bremsstrahlung, in particular, provide smoking gun signatures. We perform a dedicated search for the latter in the data taken by the Fermi gamma-ray space telescope during its first 43 months. To this end, we use a new adaptive procedure to select optimal target regions that takes into account both standard and contracted dark matter profiles. The behaviour of our statistical method is tested by a subsampling analysis of the full sky data and found to reproduce the theoretical expectations very well. The limits on the dark matter annihilation cross-section that we derive are stronger than what can be obtained from the observation of dwarf galaxies and, at least for the model considered here, collider searches. While these limits are still not quite strong enough to probe annihilation rates expected for thermally produced dark matter, future prospects to do so are very good. In fact, we already find a weak indication, with a significance of 3.1σ (4.3σ) when (not) taking into account the look-elsewhere effect, for an internal bremsstrahlung-like signal that would correspond to a dark matter mass of ∼150 GeV; the same signal is also well fitted by a gamma-ray line at around 130 GeV. Although this would be a fascinating possibility, we caution that a much more dedicated analysis and additional data will be necessary to rule out or confirm this option.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

A tentative gamma-ray line from Dark Matter annihilation at the Fermi Large Area Telescope

The observation of a gamma-ray line in the cosmic-ray fluxes would be a smoking-gun signature for dark matter annihilation or decay in the Universe. We present an improved search for such signatures in the data of the Fermi Large Area Telescope (LAT), concentrating on energies between 20 and 300 GeV. Besides updating to 43 months of data, we use a new data-driven technique to select optimized target regions depending on the profile of the Galactic dark matter halo. In regions close to the Galactic center, we find a 4.6σ indication for a gamma-ray line at E{sub γ} ≈ 130 GeV. When taking into account the look-elsewhere effect the significance of the observed excess is 3.2σ. If interpreted in terms of dark matter particles annihilating into a photon pair, the observations imply a dark matter mass of m{sub χ} = 129.8±2.4 {sup +7}{sub −13} GeV and a partial annihilation cross-section of (σv){sub χχ} {sub →} {sub γγ} = (1.27±0.32 {sup +0.18}{sub −0.28}) × 10{sup −27}cm{sup 3}s{sup −1} when using the Einasto dark matter profile. The evidence for the signal is based on about 50 photons; it will take a few years of additional data to clarify its existence.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Antiproton bounds on dark matter annihilation from a combined analysis using the DRAGON2 code

Abstract Early studies of the AMS-02 antiproton ratio identified a possible excess over the expected astrophysical background that could be fit by the annihilation of a weakly interacting massive particle (WIMP). However, recent efforts have shown that uncertainties in cosmic-ray propagation, the antiproton production cross-section, and correlated systematic uncertainties in the AMS-02 data, may combine to decrease or eliminate the significance of this feature. We produce an advanced analysis using the DRAGON2 code which, for the first time, simultaneously fits the antiproton ratio along with multiple secondary cosmic-ray flux measurements to constrain astrophysical and nuclear uncertainties. Compared to previous work, our analysis benefits from a combination of: (1) recently released AMS-02 antiproton data, (2) updated nuclear fragmentation cross-section fits, (3) a rigorous Bayesian parameter space scan that constrains cosmic-ray propagation parameters.We find no statistically significant preference for a dark matter signal and set strong constraints on WIMP annihilation tobb̅, ruling out annihilation at the thermal cross-section for dark matter masses below ∼ 200 GeV. We do find a positive residual that is consistent with previous work, and can be explained by a ∼ 70 GeV WIMP annihilating below the thermal cross-section. However, our default analysis finds this excess to have a local significance of only 2.8σ, which is decreased to 1.8σwhen the look-elsewhere effect is taken into account.

Astronomy & Astrophysics↗
DOE OSTI2020

Candidate Periodically Variable Quasars from the Dark Energy Survey and the Sloan Digital Sky Survey

Periodically variable quasars have been suggested as close binary supermassive black holes. We present a systematic search for periodic light curves in 625 spectroscopically confirmed quasars with a median redshift of 1.8 in a 4.6 deg 2 overlapping region of the Dark Energy Survey Supernova (DES-SN) fields and the Sloan Digital Sky Survey Stripe 82 (SDSS-S82). Our sample has a unique 20-year long multi-color ( griz ) light curve enabled by combining DES-SN Y6 observations with archival SDSS-S82 data. The deep imaging allows us to search for periodic light curves in less luminous quasars (down to r ~23.5 mag) powered by less massive black holes (with masses ≳ 10 8.5 M ⊙ ) at high redshift for the first time. We find five candidates with significant (at >99.74% single-frequency significance in at least two bands with a global p-value of ~7 × 10 -4 –3× 10 -3 accounting for the look-elsewhere effect) periodicity with observed periods of ~3–5 years (i.e., 1–2 years in rest frame) having ~4–6 cycles spanned by the observations. If all five candidates are periodically variable quasars, this translates into a detection rate of |${\sim }0.8^{+0.5}_{-0.3}$| % or |${\sim }1.1^{+0.7}_{-0.5}$| quasar per deg 2 . Our detection rate is 4–80 times larger than those found by previous searches using shallower surveys over larger areas. This discrepancy is likely caused by differences in the quasar populations probed and the survey data qualities. Furthermore, we discuss implications on the future direct detection of low-frequency gravitational waves. Additionally, continued photometric monitoring will further assess the robustness and characteristics of these candidate periodic quasars to determine their physical origins.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Study of γ γ → γ ψ ( 2 S ) at Belle

Using 980 fb -1 of data at and around the Υ(nS)(n = 1, 2, 3, 4, 5) resonances collected with the Belle detector at the KEKB asymmetric-energy e+e- collider, the two-photon process γγ → γψ(2S) is studied from the threshold to 4.2 GeV for the first time. Two structures are seen in the invariant mass distribution of γψ(2S): one at M R 1 = 3922.4 ± 6.5 ± 2.0 MeV/c 2 with a width of Γ R 1 = 22 ± 17 ± 4 MeV, and another at M R 2 = 4014.3 ± 4.0 ± 1.5 MeV/c 2 with a width of Γ R 2 = 4 ± 11 ± 6 MeV; the signals are parametrized with the incoherent sum of two Breit- Wigner functions. The first structure is consistent with the X(3915) or the χ c2 (3930), and the local statistical significance is determined to be 3.1σ with the systematic uncertainties included. The second matches none of the known charmonium or charmonium like states, and its global significance is determined to be 2.8σ including the look-elsewhere effect. The production rates are Γ γγ B(R 1 → γψ(2S)) = 9.8 ± 3.6 ± 1.2 eV assuming (J PC , |λ|) = (0 ++ , 0) or 2.0 ± 0.7 ± 0.2 eV with (2 ++ , 2) for the first structure and Γ γγ B(R 2 → γψ(2S)) = 6.2 ± 2.2 ± 0.8 eV with (0 ++ , 0) or 1.2 ± 0.4 ± 0.2 eV with (2 ++ , 2) for the second one. Furthermore, the first errors are statistical and the second systematic, and λ is the helicity.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2012

Search for a fermiophobic Higgs boson in the diphoton decay channel with the ATLAS detector

A search for a fermiophobic Higgs boson using diphoton events produced in proton-proton collisions at a centre-of-mass energy of √s = 7 TeV is performed using data corresponding to an integrated luminosity of 4.9 fb -1 collected by the ATLAS experiment at the Large Hadron Collider. A specific benchmark model is considered where all the fermion couplings to the Higgs boson are set to zero and the bosonic couplings are kept at the Standard Model values (fermiophobic Higgs model). The largest excess with respect to the background-only hypothesis is found at 125.5 GeV, with a local significance of 2.9 standard deviations, which reduces to 1.6 standard deviations when taking into account the look-elsewhere effect. The data exclude the fermiophobic Higgs model in the ranges 110.0–118.0 GeV and 119.5–121.0 GeV at 95 % confidence level.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2012

Search for the Standard Model Higgs boson in the decay channel H -> ZZ((*)) -> 4l with 4.8 fb(-1) of pp collision data at root s=7 TeV with ATLAS

This Letter presents a search for the Standard Model Higgs boson in the decay channel H {yields} ZZ{sup (*)} {yields} {ell}{sup +}{ell}{sup -}{ell}{prime}{sup +}{ell}{prime}{sup -}, where {ell}, {ell}{prime} = e or {mu}, using proton-proton collisions at {radical}s = 7 TeV recorded with the ATLAS detector and corresponding to an integrated luminosity of 4.8 fb{sup -1}. The four-lepton invariant mass distribution is compared with Standard Model background expectations to derive upper limits on the cross section of a Standard Model Higgs boson with a mass between 110 GeV and 600 GeV. The mass ranges 134-156 GeV, 182-233 GeV, 256-265 GeV and 268-415 GeV are excluded at the 95% confidence level. The largest upward deviations from the background-only hypothesis are observed for Higgs boson masses of 125 GeV, 244 GeV and 500 GeV with local significances of 2.1, 2.2 and 2.1 standard deviations, respectively. Once the look-elsewhere effect is considered, none of these excesses are significant.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Statistical Association between the Candidate Repeating FRB 20200320A and a Galaxy Group

Abstract We present results from angular cross correlations between select samples of CHIME/FRB repeaters and galaxies in three photometric galaxy surveys, which have shown correlations with the first CHIME/FRB catalog containing repeating and nonrepeating sources: Wide-field Infrared Survey Explorer (WISE) × SCOS, DESI-BGS, and DESI-LRG. We find a statistically significant correlation (p-value <0.001, after accounting for look-elsewhere factors) between a sample of repeaters with an extragalactic dispersion measure (DM) > 395 pc cm −3 and WISE × SCOS galaxies with redshiftz> 0.275. We demonstrate that the correlation arises surprisingly because of a statistical association between FRB 20200320A (extragalactic DM ≈ 550 pc cm −3 ) and a galaxy group in the same dark matter halo at redshiftz≈ 0.32. We estimate that the host halo, along with an intervening halo at redshiftz≈ 0.12, accounts for at least ∼30% of the extragalactic DM. Our results strongly motivate incorporating galaxy group and cluster catalogs into direct host association pipelines for FRBs with ≲ 1 ′ localization precision, effectively utilizing the two-point information to constrain FRB properties such as their redshift and DM distributions. In addition, we find marginal evidence for a negative correlation at 99.4% confidence limit between a sample of repeating FRBs with baseband data (median extragalactic DM = 354 pc cm −3 ) and DESI-LRG galaxies with redshift 0.3 ≤z< 0.45, suggesting that the repeaters might be more prone than apparent nonrepeaters to propagation effects in FRB–galaxy correlations due to intervening free electrons over angular scales ∼0.°5.

Astronomy & Astrophysics↗