Limits and Confidence Intervals in the Presence of Nuisance Parameters

Abstract

We study the frequentist properties of confidence intervals computed by the method known to statisticians as the Profile Likelihood. It is seen that the coverage of these intervals is surprisingly good over a wide range of possible parameter values for important classes of problems, in particular whenever there are additional nuisance parameters with statistical or systematic errors. Programs are available for calculating these intervals.

6 figures

References in corpus (5)

• A Unified Approach to the Classical Statistical Analysis of Small Signals
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• Confidence Intervals and Upper Bounds for Small Signals in the Presence of Background Noise
• On Bayesian Treatment of Systematic Uncertainties in Confidence Interval Calculation
• Correcting the Minimization Bias in Searches for Small Signals

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• The Majorana Demonstrator's Search for Double-Beta Decay of ${}^{76}$Ge to Excited States of ${}^{76}$Se
• Study of the GeV to TeV morphology of the $\gamma$-Cygni SNR (G78.2+2.1) with MAGIC and Fermi-LAT
• Search for $B$ Mesogenesis at BABAR
• Identification of gamma-ray emission from 3C345 and NRAO512
• Multiwavelength study of the gravitationally lensed blazar QSO B0218+357 between 2016 and 2020
• Probing Flavor Structure of Cosmic Ray $e^{\mp }$ Spectrum and Implications for Dark Matter Indirect Searches
• MAGIC and Fermi-LAT gamma-ray results on unassociated HAWC sources
• When The Standard Model Higgs Meets Its Lighter 95 GeV Twin
• Direct Measurement of Astrophysically Important Resonances in ${}^{38}\mathrm{K}(p,\gamma ){}^{39}\mathrm{Ca}$
• A strong limit on the very-high-energy emission from GRB 150323A
• Lectures on Statistics in Theory: Prelude to Statistics in Practice
• Gamma-ray and Synchrotron Radiation from Dark Matter annihilations in Ultra-faint Dwarf Galaxies
• Probing dark gauge boson with observations from neutron stars
• Search for baryon and lepton number violating decays $D^0\to \bar{p}{e}^{+}$ and $D^0\to p{e}^{-}$
• Prospects for $\gamma$-ray observations of the Perseus galaxy cluster with the Cherenkov Telescope Array
• Search for a new 17 MeV resonance via $e^{+}{e}^{-}$ annihilation with the PADME Experiment
• VERITAS Observations of Six Bright, Hard-Spectrum Fermi-LAT Blazars
• A Search for Very High-Energy Gamma Rays from the Missing Link Binary Pulsar J1023+0038 with VERITAS
• Turbulent spectra of the brightest gamma-ray flares of blazars
• Searching for Gamma-Ray Emission from Reticulum II by Fermi-LAT
• Search for the lepton number violating decay ${\Sigma }^{-}\to p{e}^{-}{e}^{-}$ and the rare inclusive decay ${\Sigma }^{-}\to {\Sigma }^{+}X$
• Signal estimation in On/Off measurements including event-by-event variables
• A Search for Pulsed Very High-Energy Gamma Rays from Thirteen Young Pulsars in Archival VERITAS Data
• Recommended conventions for reporting results from direct dark matter searches
• Statistical Tools for Imaging Atmospheric Cherenkov Telescopes
• Objective Bayesian analysis of "on/off" measurements
• Analysis of Fermi-LAT data from Tucana-II: Possible constraints on the Dark Matter models with an intriguing hint of a signal
• Galaxy cluster constraints on the coupling to photons of low-mass scalars
• Multiwavelength analysis of low surface brightness galaxies to study possible dark matter signature
• Multi-Wavelength Observation Campaign of the TeV Gamma-Ray Binary HESS J0632+057 with NuSTAR, VERITAS, MDM, and Swift
• Search for the decay ${\chi }_{c1}(3872)\to {\pi }^{+}{\pi }^{-}{\chi }_{c1}$
• VERITAS and Fermi-LAT constraints on the Gamma-ray Emission from Superluminous Supernovae SN2015bn and SN2017egm
• A direct measurement of the 17O(a,g)21Ne reaction in inverse kinematics and its impact on heavy element production
• Search for $\bar{\Lambda }$-$\Lambda$ oscillations in the decay $J/\psi \to p{K}^{-}\bar{\Lambda }+c.c.$
• Evidence for longitudinally polarized $W$ bosons in the electroweak production of same-sign $W$ boson pairs in association with two jets in pp collisions at $\sqrt{s}=13$ TeV with the ATLAS detector
• Using $\gamma$-ray observations of dwarf spheroidal galaxies to test the possible common origin of the W-boson mass anomaly and the GeV $\gamma$-ray/antiproton excesses
• Search for charge nonconservation and Pauli exclusion principle violation with the Majorana Demonstrator
• Prospects for studies of $D^{\ast 0}\to {\mu }^{+}{\mu }^{-}$ and $B_{(s)}^{\ast 0}\to {\mu }^{+}{\mu }^{-}$ decays
• Observation of the Black Widow B1957+20 millisecond pulsar binary system with the MAGIC telescopes
• Higgs production in $e^{-}{e}^{+}$ collisions as a probe of noncommutativity
• Bayesian Approach for Counting Experiment Statistics applied to a Neutrino Point Source Analysis
• Branching fraction measurement of $J/\psi \to K_S{K}_L$ and search for $J/\psi \to K_S{K}_S$
• Search for two neutrino double electron capture of ${}^{124}$Xe and ${}^{126}$Xe in the full exposure of the LUX detector
• Constraints on Axion-like Particles from the gamma-ray observation of the Galactic Center
• Temporal and Spectral Study of PKS B1222+216 Flares in 2014
• Combination of searches for singly and doubly charged Higgs bosons produced via vector-boson fusion in proton-proton collisions at $\sqrt{s}=13$ TeV with the ATLAS detector
• A search for the anomalous events detected by ANITA using the Pierre Auger Observatory
• Search for the semi-leptonic decays ${\Lambda }_c^{+}\to \Lambda {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ and ${\Lambda }_c^{+}\to p{K}_S^0{\pi }^{-}{e}^{+}{\nu }_e$
• Very-high-energy gamma-ray observations of the Type Ia Supernova SN 2014J with the MAGIC telescopes
• MAGIC search for VHE $\gamma$-ray emission from AE Aquarii in a multiwavelength context
• Measurement of vector boson production cross sections and their ratios using $pp$ collisions at $\sqrt{s}=13.6$ TeV with the ATLAS detector
• First search for the ${\eta }_{c2}(1D)$ in $B$ decays at Belle
• Neutrino Flavor Transformations from New Short-Range Forces
• Search for $B^0$ Decays to Invisible Final States ($+\gamma$) at Belle
• MAGIC Upper Limits for two Milagro-detected, Bright Fermi Sources in the Region of SNR G65.1+0.6
• VERITAS and multiwavelength observations of the Blazar B3 2247+381 in response to an IceCube neutrino alert
• Constraints on the R-Parity-violating minimal supersymmetric standard model with neutrino masses from multilepton studies at the LHC
• Discovery of very-high-energy emission from RGB J2243+203 and derivation of its redshift upper limit
• Sensitivity study of the charged lepton flavor violating process $\tau \to \gamma \mu$ at STCF
• Performance data from the ZEPLIN-III second science run
• Experimental study of the ${}^{11}\text{B}(p,3\alpha )\gamma$ reaction at $E_p=0.5-2.7$ MeV
• Assessing Uncertainties in the Predicted Very-High-Energy Flux of Globular Clusters in the Cherenkov Telescope Array Era
• Search for TeV emission from the Fermi Bubbles at low Galactic latitudes with H.E.S.S. inner Galaxy survey observations
• Search for Darkonium in $e^{+}{e}^{-}$ Collisions
• Upper limits for the photoproduction cross section for the Phi--(1860) pentaquark state off the deuteron
• Constraining the distribution of dark matter in inner galaxy with indirect detection signal: The case of tentative 130 gev γ-ray line
• On Bayesian analysis of on-off measurements
• Constraints on Axion-Like Particles from VERITAS Observations of a Flaring Radio Galaxy in the Perseus Cluster
• Measurement of the absolute branching fraction of the three-body decay ${\Lambda }_c^{+}\to {\Xi }^0{K}^{+}{\pi }^0$ and search for ${\Lambda }_c^{+}\to n{K}^{+}{\pi }^0$, ${\Sigma }^0{K}^{+}{\pi }^0$ and $\Lambda K^{+}{\pi }^0$
• An Archival Search for Neutron-Star Mergers in Gravitational Waves and Very-High-Energy Gamma Rays
• Study of $e^{+}{e}^{-}\to {\pi }^{0}X(3872)\gamma$ and search for $Z_c(4020{)}^0\to X(3872)\gamma$
• Hawking Radiation of Nonrelativistic Scalars: Applications to Pion and Axion Production
• Search for the rare decay of $\psi (3686)\to {\Lambda }_c^{+}\overline{p}{e}^{+}{e}^{-}+c.c.$ at BESIII
• Very-high-energy observations of the Seyfert galaxy NGC 4151 with MAGIC -- Indication of another gamma-ray obscured candidate neutrino source
• Search for baryon and lepton number violating decays of ${\Xi }^0$ hyperons
• Constraints on VHE gamma-ray emission of Flat Spectrum Radio Quasars with the MAGIC telescopes
• DarkFlux: A new tool to analyze indirect-detection spectra of next-generation dark matter models
• Search for the radiative transition ${\chi }_{c1}(3872)\to \gamma {\psi }_2(3823)$
• Search for the lepton number violation decay $\varphi \to {\pi }^{+}{\pi }^{+}{e}^{-}{e}^{-}$ via $J/\psi \to \varphi \eta$
• Results from MAGIC's first observation cycle on galactic sources
• Combined search in dwarf spheroidal galaxies for branon dark matter annihilation signatures with the MAGIC telescopes
• Testing the ubiquitous presence of very high energy emission in gamma-ray bursts with the MAGIC telescopes
• H.E.S.S. detection and multi-wavelength study of the $z\sim$ 1 blazar PKS 0346$-$27
• First detection of VHE gamma-ray signal from the FSRQ TON 0599
• Optimal Adaptive Nonparametric Denoising of Multidimensional - Time Signal
• The H.E.S.S. extragalactic sky survey with the first decade of observations
• Calculating a confidence interval on the sum of binned leakage
• Search for the reaction $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\chi }_{cJ}$ and a charmonium-like structure decaying to ${\chi }_{cJ}{\pi }^{\pm }$ between 4.18 and 4.60 GeV
• H.E.S.S. programme searching for VHE gamma rays associated with FRBs
• Control and measurement of electric dipole moments in levitated optomechanics
• Extended Higgs-portal dark matter and the Fermi-LAT Galactic Center Excess
• Constraints on axion-like particles from ultra-high-energy observations of M87 with the HAWC observatory
• Recasting and Forecasting Dark Matter Limits Without Raw Data: A Generalized Algorithm for Gamma-Ray Telescopes
• Robust Lifetime Estimation from HPGe Radiation-Sensor Time Series Using Pairwise Ratios and MFV Statistics
• On Integral Upper Limits Assuming Power Law Spectra and the Sensitivity in High-Energy Astronomy
• Multiplicative scale uncertainties in the unified approach for constructing confidence intervals
• A Test for the Presence of a Signal
• A Comparison of Limit Setting Methods for the On-Off Problem
• A Test for the Presence of a Signal, with Multiple Channels and Marked Poisson
• Search for $J/\psi \to K_S^0{K}_S^0$ and $\psi (3686)\to K_S^0{K}_S^0$
• Searching for dark matter annihilating into light long-lived mediators from stars inside dwarf spheroidal galaxies
• Search for the leptonic decays $D^{\ast +}\to e^{+}{\nu }_e$ and $D^{\ast +}\to {\mu }^{+}{\nu }_{\mu }$
• Behavioral event detection and rate estimation for autonomous vehicle evaluation
• Extragalactic Searches for Dark Matter Annihilation
• Adding a systematic uncertainty to the signal estimation in the on/off-zone measurements
• Search for the charged lepton flavor violating decay $\psi (3686)\to e^{\pm }{\mu }^{\mp }$
• Observation of double parton scattering in same-sign W boson pair production in pp collisions at $\sqrt{s}=13$ TeV with the ATLAS detector
• Can local White Dwarfs constrain Dark Matter interactions?
• Search for the baryon and lepton number violating decay $J/\psi \to p{e}^{-}$ + c.c
• Observation of burst activity from SGR1935+2154 associated to first galactic FRB with H.E.S.S
• Stochastic Properties of Ultralight Scalar Field Gradients
• Search for the $e^{+}{e}^{-}\to \varphi {\chi }_{c1}(3872)$ process at BESIII
• Correlating Gravitational Wave and Gamma-ray Signals from Primordial Black Holes
• On a chi^2-function with previously estimated background
• The second H.E.S.S. gamma-ray burst catalogue: 15 years of observations with the H.E.S.S. telescopes
• Statistical treatment of searches for counterparts of positionally-uncertain astrophysical sources: from flux upper limits to detection
• Revising Indirect Dark Matter Constraints with Updated Astrophysical $J$-Factor Priors
• Search for Dark Matter in Upsilon Decays at BABAR Experiment
• Long-term study of the gamma-ray emission of Cygnus X-3 with MAGIC and Fermi-LAT
• A Bayesian on-off analysis of cosmic ray data
• Study of $e^{+}{e}^{-}\to h^{+}{h}^{-}J/\psi (h=\pi ,K,p)$ via initial-state radiation at Belle~II
• Coherently Enhanced Axion-Photon Conversion via Seeded Photons for Short-Pulse Axion Detection
• Search for the lepton number violating decay $\eta \to {\pi }^{+}{\pi }^{+}{e}^{-}{e}^{-}+c.c.$ via $J/\psi \to \varphi \eta$
• Search for Higgs bosons produced in association with a high-energy photon via vector-boson fusion and decaying to a pair of $b$-quarks in the ATLAS detector
• On sensitivity calculations for neutrino oscillation experiments