Tuning goodness-of-fit tests†
Abstract
As modern precision cosmological measurements continue to show agreement with the broad features of the standard Λ cold dark matter (ΛCDM) cosmological model, we are increasingly motivated to look for small departures from the standard model’s predictions that might not be detected with standard approaches. While searches for extensions and modifications of ΛCDM have to date turned up no convincing evidence of beyond-the-standard-model cosmology, the list of models compared against ΛCDM is by no means complete and is often governed by readily coded modifications to standard Boltzmann codes. Also, standard goodness-of-fit methods such as a naive χ2 test fail to put strong pressure on the null hypothesis, since modern data sets have orders of magnitudes more degrees of freedom than the null hypothesis. Here we present a method of tuning goodness-of-fit tests to detect potential subdominant extra-ΛCDM signals present in the data through compressing observations in a way that maximizes extra-ΛCDM signal variation over noise and ΛCDM variation. This method, based on a Karhunen–Loève transformation of the data, is tuned to be maximally sensitive to particular types of variations characteristic of the tuning model, but unlike direct model comparison, the test is also sensitive to features that only partially mimicmore »
- Authors:
-
[1];
- Department of Physics, University of California, Davis One Shields Ave, Davis, CA 95616, USA
- Department of Statistics, University of California, Davis One Shields Ave, Davis, CA 95616, USA
- Publication Date:
- Research Org.:
- Univ. of California, Davis, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1492122
- Alternate Identifier(s):
- OSTI ID: 1611318
- Grant/Contract Number:
- SC-0009999; SC0019081; SC0009999
- Resource Type:
- Published Article
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Additional Journal Information:
- Journal Name: Monthly Notices of the Royal Astronomical Society Journal Volume: 484 Journal Issue: 2; Journal ID: ISSN 0035-8711
- Publisher:
- Royal Astronomical Society
- Country of Publication:
- United Kingdom
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; Astronomy & Astrophysics; methods: statistical; cosmic background radiation
Citation Formats
Arrasmith, A., Follin, B., Anderes, E., and Knox, L. Tuning goodness-of-fit tests†. United Kingdom: N. p., 2019.
Web. doi:10.1093/mnras/stz066.
Arrasmith, A., Follin, B., Anderes, E., & Knox, L. Tuning goodness-of-fit tests†. United Kingdom. https://doi.org/10.1093/mnras/stz066
Arrasmith, A., Follin, B., Anderes, E., and Knox, L. Wed .
"Tuning goodness-of-fit tests†". United Kingdom. https://doi.org/10.1093/mnras/stz066.
@article{osti_1492122,
title = {Tuning goodness-of-fit tests†},
author = {Arrasmith, A. and Follin, B. and Anderes, E. and Knox, L.},
abstractNote = {As modern precision cosmological measurements continue to show agreement with the broad features of the standard Λ cold dark matter (ΛCDM) cosmological model, we are increasingly motivated to look for small departures from the standard model’s predictions that might not be detected with standard approaches. While searches for extensions and modifications of ΛCDM have to date turned up no convincing evidence of beyond-the-standard-model cosmology, the list of models compared against ΛCDM is by no means complete and is often governed by readily coded modifications to standard Boltzmann codes. Also, standard goodness-of-fit methods such as a naive χ2 test fail to put strong pressure on the null hypothesis, since modern data sets have orders of magnitudes more degrees of freedom than the null hypothesis. Here we present a method of tuning goodness-of-fit tests to detect potential subdominant extra-ΛCDM signals present in the data through compressing observations in a way that maximizes extra-ΛCDM signal variation over noise and ΛCDM variation. This method, based on a Karhunen–Loève transformation of the data, is tuned to be maximally sensitive to particular types of variations characteristic of the tuning model, but unlike direct model comparison, the test is also sensitive to features that only partially mimic the tuning model. As an example of its use, we apply this method in the context of a non-standard primordial spectrum compared against the 2015 Planck cosmic microwave background temperature power spectrum. We find no evidence for extra-ΛCDM physics.},
doi = {10.1093/mnras/stz066},
journal = {Monthly Notices of the Royal Astronomical Society},
number = 2,
volume = 484,
place = {United Kingdom},
year = {Wed Jan 09 00:00:00 EST 2019},
month = {Wed Jan 09 00:00:00 EST 2019}
}
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Works referenced in this record:
Signal-to-Noise Eigenmode Analysis of the Two-Year COBE Maps
journal, May 1995
- Bond, J. Richard
- Physical Review Letters, Vol. 74, Issue 22
CMB constraints on principal components of the inflaton potential
journal, August 2010
- Dvorkin, Cora; Hu, Wayne
- Physical Review D, Vol. 82, Issue 4
Measurement of the cosmic microwave background spectrum by the COBE FIRAS instrument
journal, January 1994
- Mather, J. C.; Cheng, E. S.; Cottingham, D. A.
- The Astrophysical Journal, Vol. 420
Planck 2015 results : XI. CMB power spectra, likelihoods, and robustness of parameters
journal, September 2016
- Aghanim, N.; Arnaud, M.; Ashdown, M.
- Astronomy & Astrophysics, Vol. 594
Encyclopædia Inflationaris
journal, December 2014
- Martin, Jérôme; Ringeval, Christophe; Vennin, Vincent
- Physics of the Dark Universe, Vol. 5-6
Planck 2013 results. XXII. Constraints on inflation
journal, October 2014
- Ade, P. A. R.; Aghanim, N.; Armitage-Caplan, C.
- Astronomy & Astrophysics, Vol. 571
Planck 2015 results : XIII. Cosmological parameters
journal, September 2016
- Ade, P. A. R.; Aghanim, N.; Arnaud, M.
- Astronomy & Astrophysics, Vol. 594
Principal power of the CMB
journal, February 2004
- Hu, Wayne; Okamoto, Takemi
- Physical Review D, Vol. 69, Issue 4
Model-independent reionization observables in the CMB
journal, July 2003
- Hu, Wayne; Holder, Gilbert P.
- Physical Review D, Vol. 68, Issue 2
Planck 2015 results : I. Overview of products and scientific results
journal, September 2016
- Adam, R.; Ade, P. A. R.; Aghanim, N.
- Astronomy & Astrophysics, Vol. 594
QUANTIFYING DISCORDANCE IN THE 2015 PLANCK CMB SPECTRUM
journal, February 2016
- Addison, G. E.; Huang, Y.; Watts, D. J.
- The Astrophysical Journal, Vol. 818, Issue 2
Searching for dark matter in the CMB: A compact parametrization of energy injection from new physics
journal, February 2012
- Finkbeiner, Douglas P.; Galli, Silvia; Lin, Tongyan
- Physical Review D, Vol. 85, Issue 4
Estimating the power spectrum of the cosmic microwave background
journal, February 1998
- Bond, J. R.; Jaffe, A. H.; Knox, L.
- Physical Review D, Vol. 57, Issue 4
Planck intermediate results : LI. Features in the cosmic microwave background temperature power spectrum and shifts in cosmological parameters
journal, November 2017
- Aghanim, N.; Akrami, Y.; Ashdown, M.
- Astronomy & Astrophysics, Vol. 607
NINE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE ( WMAP ) OBSERVATIONS: FINAL MAPS AND RESULTS
journal, September 2013
- Bennett, C. L.; Larson, D.; Weiland, J. L.
- The Astrophysical Journal Supplement Series, Vol. 208, Issue 2