Statistics: Handle with Care, Detecting Multiple Model Components with the Likelihood Ratio Test

Abstract

The likelihood ratio test (LRT) and the related $F$ test, do not (even asymptotically) adhere to their nominal ${\chi }^2$ and $F$ distributions in many statistical tests common in astrophysics, thereby casting many marginal line or source detections and non-detections into doubt. Although there are many legitimate uses of these statistics, in some important cases it can be impossible to compute the correct false positive rate. For example, it has become common practice to use the LRT or the $F$ test for detecting a line in a spectral model or a source above background despite the lack of certain required regularity conditions. In these and other settings that involve testing a hypothesis that is on the boundary of the parameter space, {\it contrary to common practice, the nominal ${\chi }^2$ distribution for the LRT or the $F$ distribution for the $F$ test should not be used}. In this paper, we characterize an important class of problems where the LRT and the $F$ test fail and illustrate this non-standard behavior. We briefly sketch several possible acceptable alternatives, focusing on Bayesian posterior predictive probability-values. We present this method in some detail, as it is a simple, robust, and intuitive approach. This alternative method is illustrated using the gamma-ray burst of May 8, 1997 (GRB 970508) to investigate the presence of an Fe K emission line during the initial phase of the observation.

Twenty four pages, seven figures. The Astrophysical Journal, May 2002, to appear

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• Chandra and NuSTAR follow-up observations of Swift-BAT selected AGN
• The role of grain size in AGN torus dust models
• Spectral evolution of the X-ray nova XTE J1859+226 during its outburst observed by BeppoSAX and RXTE
• XMM-Newton and INTEGRAL study of the SFXT IGR J18483-0311 in quiescence: hint of a cyclotron emission feature?
• Detecting Unspecified Structure in Low-Count Images
• Uncovering Planetary Nebulae in Early Type Galaxies using the Rutgers Fabry-Perot
• Detection capabilities of the Athena X-IFU for the warm-hot intergalactic medium using gamma-ray burst X-ray afterglows
• The $\gamma$-ray pulsar J0633+0632 in X-rays
• A Multi-Wavelength Study of the Jet, Lobes and Core of the Quasar PKS 2101-490
• Can the Fe K-alpha Line Reliably Predict Supernova Remnant Progenitors?
• Evidence for Neutrino Emission from X-Ray-bright Active Galactic Nuclei with IceCube
• Towards an informed quest for accretion disc winds in quasars: the intriguing case of Ton 28
• A comprehensive approach to analyzing the XMM-Newton data of Seyfert 1 galaxies
• Long-term X-ray Variability of the Symbiotic System RT Cru based on Chandra Spectroscopy
• New Spatially Resolved Imaging of the SR 21 Transition Disk and Constraints on the Small-Grain Disk Geometry
• Study of the GeV to TeV morphology of the $\gamma$-Cygni SNR (G78.2+2.1) with MAGIC and Fermi-LAT
• A Search for the 3.5 keV Line from the Milky Way's Dark Matter Halo with HaloSat
• A Study of the 20 Day Superorbital Modulation in the High-Mass X-ray Binary IGR J16493-4348
• Nuclear X-ray properties of the peculiar radio-loud hidden AGN 4C+29.30
• A Suzaku Observation of MCG-2-58-22: Constraining the Geometry of the Circumnuclear Material
• Chandra measurement of the X-ray spectrum of a quasar at z=5.99
• NuSTAR and XMM-Newton observations of 1E1743.1-2843: indications of a neutron star LMXB nature of the compact object
• Searching for narrow absorption and emission lines in XMM-Newton spectra of gamma-ray bursts
• Relativistic outflow in CXO CDFS J033260.0-274748
• An extended source of GeV gamma rays coincident with the supernova remnant HB 21
• Deep optical observations of unusual neutron star Calvera with the GTC
• The lively accretion disc in NGC 2992. III. Tentative evidence of rapid Ultra Fast Outflow variability
• Physical and kinematical properties of the X-ray absorber in the broad absorption line quasar APM 08279+5255
• The XMM-Newton observation of GRB 040106 : evidence for an afterglow in a wind environment
• First characterization of Swift J1845.7-0037 with NuSTAR
• Unbinned maximum-likelihood estimators for low-count data: Applications to faint X-ray spectra in the Taurus Molecular Cloud
• Broadband time-resolved spectroscopy of thermonuclear X-ray bursts from 4U 1636-536 using AstroSat
• The cooling, mass and radius of the neutron star in EXO 0748-676 in quiescence with XMM-Newton
• Gaia GraL: Gaia DR2 Gravitational Lens Systems. IV. Keck/LRIS spectroscopic confirmation of GRAL113100-441959 and model prediction of time-delays
• Discovery of a magnetic neutron star in X-ray transient IGR J01583+6713
• Evidence for thermal X-ray emission from the synchrotron dominated shocks in Tycho's supernova remnant
• An XMM-Newton study of active-inactive galaxy pairs
• XMM-Newton reveals a Seyfert-like X-ray spectrum in the z=3.6 QSO B1422+231
• TD-CARMA: Painless, accurate, and scalable estimates of gravitational-lens time delays with flexible CARMA processes
• Gamma-ray-emitting narrow-line Seyfert 1 galaxies: the Swift view
• Maximum-likelihood detection of sources among Poissonian noise
• On the peculiar properties of the narrow-line quasar PG 1543+489
• A retrograde spin of the black hole in MAXI J1659--152
• Suzaku observations of the 2013 outburst of KS 1947+300
• Thermal components in the early X-ray afterglows of GRBs: likely cocoon emission and constraints on the progenitors
• Symbiotic stars in X-rays II: faint sources detected with XMM-Newton and Chandra
• High Resolution Gratings Spectroscopy of GRBs 030382 and 041006 with Chandra LETGS
• Fast Timing Analysis of Cygnus X-1 using SPI on board INTEGRAL
• Investigating the superorbital modulations in 4U 1909+07, IGR J16418-4532 and IGR J16479-4514 with Swift XRT, BAT and NuSTAR observations
• The Spin of a Newborn Black Hole: Swift J1728.9-3613
• X-ray view of a merging supermassive black hole binary candidate SDSSJ1430+2303: Results from the first ~200 days of observations
• A sensitive search for unknown spectral emission lines in the diffuse X-ray background with XMM-Newton
• A New Ultraluminous X-ray Source in the Nearby Edge-on Spiral NGC 891
• An extreme gravitationally redshifted iron line at 4.8 keV in Mrk 876
• Hard X-ray Emission from Sh2-104: A NuSTAR search for Gamma-ray Counterparts
• The Effect of Microlensing On the Observed X-ray Energy Spectra of Gravitationally Lensed Quasars
• Constraining Models of the Pulsar Wind Nebula in SNR G0.9+0.1 via Simulation of its Detection Properties using the Cherenkov Telescope Array
• X-raying winds in distant quasars: the first high-redshift wind duty cycle
• The peculiar high-mass X-ray binary 1ES 1210-646
• A NuSTAR observation of the eclipsing binary system OAO 1657-415: The revival of the cyclotron line
• Winds in ultraluminous X-ray sources: new challenges
• Systematic errors in the maximum likelihood regression of Poisson count data: introducing the overdispersed chi-square distribution
• Short time-scale X-ray spectral variability in the Seyfert 1 galaxy NGC 3783
• Statistical Tools for Imaging Atmospheric Cherenkov Telescopes
• A search for the missing baryons with X--ray absorption lines towards the blazar 1ES 1553+113
• Anomalous X-Ray emission in GRB060904B: a Nickel line?
• Swift observations of GRB050712
• Modelling variability power spectra of active galaxies from irregular time series
• Variation of Spectral and Timing Properties in the Extended Burst Tails from the Magnetar 4U 0142+61
• The High Energy X-ray Probe (HEX-P): Studying Extreme Accretion with Ultraluminous X-ray Sources
• A search for lines in the bright X-ray afterglow of GRB120711A
• Revisit the Circumnuclear X-ray Emission of NGC 2992 in a Historically Low State
• Possible TeV $\gamma$-ray binary origin of HESS J1828-099
• The broad-band spectrum of the Narrow-line Seyfert 1 NGC 4748: from UV to hard X-ray
• A Study of Low-Mass X-Ray Binaries in the Low-Luminosity Regime
• X-ray monitoring of gravitationally lensed radio-loud quasars with Chandra
• The XMM-Newton and NuSTAR view of IRASF11119+3257. I Detection of multiple UFO components and a very cold corona
• Modeling the multiwavelength emission from G73.9+0.9: Gamma-rays from a SNR-MC interaction
• NuSTAR observation of GRO J1744-28 at low mass accretion rate
• Consistency Tests for Comparing Astrophysical Models and Observations
• Signs of magnetic acceleration and multi-zone emission in GRB 080825C
• An independent search for annual modulation and its significance in ANAIS-112 data
• Four ages of rotating stars in the rotation--activity relationship and gyrochronology
• On the apparent absence of broad iron lines in Seyfert galaxies
• An XMM-Newton view of the X-ray flat radio-quiet quasar PG 1416-129
• Limits on Leptonic TeV Emission from the Cygnus Cocoon with Swift-XRT
• Hard X-Ray broadband spectroscopy of Mrk 876: characterizing its spectrum
• X-ray Activity Variations and Coronal Abundances of the Star-Planet Interaction candidate HD 179949
• Constraining coronal heating: employing Bayesian analysis techniques to improve the determination of solar atmospheric plasma parameters
• Data-Space Validation of High-Dimensional Models by Comparing Sample Quantiles
• Winds of change: the nuclear and galaxy-scale outflows and the X-ray variability of 2MASS 0918+2117
• X-ray spectral properties of the accreting millisecond pulsar IGR J17498-2921 during its 2023 outburst
• The NuSTAR view of the Seyfert Galaxy HE 0436-4717
• X-ray study of high-and-low luminosity modes and peculiar low-soft-and-hard activity in the transitional pulsar XSS J12270-4859
• Probable evidence for a transient mega-electron volt emission line in the GRB 221023A
• X-ray properties of high-redshift Radio Loud and Radio Quiet Quasars observed by Chandra
• Deep $Chandra$ observations of the NGC 4472 globular cluster black hole XMMU 122939.7+075333: Short term variability from the first globular cluster black hole binary
• A New Result on the Origin of the Extragalactic Gamma-ray Background
• The Star Formation Reference Survey. IV. Stellar mass distribution of local star-forming galaxies
• Long term variability of Swift J1753.5-0127]{Long term variability of Swift J1753.5-0127: X-ray spectral-temporal correlations during state transitions
• X-raying the coronae of HD~155555
• Emission and Absorption Lines in Photospheric Radius Expansion Bursts of 4U 1820$-$30
• Maximum-likelihood regression with systematic errors for astronomy and the physical sciences: II. Hypothesis testing of nested model components for Poisson data
• NGC 2403 XMM4: evidence for a super-Eddington neutron star with a possible transient pulsation
• Bayesian analysis of multiple direct detection experiments
• Matched-filtering Line Search Methods Applied to Suzaku Data
• Realizing the potential of astrostatistics and astroinformatics
• The INTEGRAL view of Gamma-Ray Bursts
• Long-term study of the Double Pulsar J0737-3039 with XMM-Newton: spectral analysis
• Spectral fit residuals as an indicator to increase model complexity
• Six Maxims of Statistical Acumen for Astronomical Data Analysis
• AstroSat observation of the magnetar SGR J1830$-$0645 during its first detected X-ray outburst
• Multiphase Powerful Outflows Detected in High-z Quasars
• Spectral evolution of X-ray pulsar 4U 1901+03 during the 2019 outburst based on Insight-HXMT and NuSTAR observations
• Hard X-ray view of two $\gamma$-ray detected low-luminosity active galactic nuclei: NGC 315 and NGC 4261
• Cross-disciplinary research in astronomy
• Observation of the Crab Nebula with the Single-Mirror Small-Size Telescope stereoscopic system at low altitude
• Identification of high-energy astrophysical point sources via hierarchical Bayesian nonparametric clustering
• iid2022: A Workshop on Statistical Methods for Event Data in Astronomy
• Unveiling the biconical geometry of the outflow in the ultraluminous X-ray source NGC 5204 X-1
• On the future of astrostatistics: statistical foundations and statistical practice
• Future Detections of the Warm-Hot Intergalactic Medium using Bright Power Law Sources with NewAthena
• Probing spectral variability in NGC 4490 ULX-8 over 24 years of XMM-Newton, Chandra and Swift-XRT observations
• Chandra X-ray Observatory study of the X-ray emission of PKS 0023-26 and comparison with recent ALMA results
• Long Term Studies of Z sources with HEXTE/RXTE
• The Suzaku view of highly-ionised outflows in AGN