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Improved Cosmological Constraints from a Bayesian Hierarchical Model of Supernova Type Ia Data

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Astrostatistical Challenges for the New Astronomy

Part of the book series: Springer Series in Astrostatistics ((SSIA,volume 1))

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Abstract

We present a Bayesian hierarchical model for inferring the cosmological parameters from the supernovae type Ia fitted with the SALT-II lightcurve fitter. We demonstrate with simulated data sets that our method delivers tighter statistical constraints on the cosmological parameters over 90% of the time, that it reduces statistical bias typically by a factor ~2–3 and that it has better coverage properties than the usual χ 2 approach. As a further benefit, a full posterior probability distribution for the dispersion of the intrinsic magnitude of SNe is obtained. We apply this method to recent SNIa data, and by combining them with CMB and BAO data we obtain Ωm = 0:28 ± 0:02, ΩΛ = 0:73 ± 0:01 (assuming ω = −1) and Ω m = 0:28 ± 0:01, ω = −0:90 ± 0:05 (assuming flatness; statistical uncertainties only). We constrain the intrinsic dispersion of the B-band magnitude of the SNIa population, obtaining \(\sigma _\mu ^{\text{int}} \) = 0:13 ± 0:01 [mag].

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Notes

  1. 1.

    1 Notice that we neglect correlations between different SNIa, which is reflected in the fact that Σ C takes a block-diagonal form. It would be however very easy to add arbitrary cross-correlations to our formalism (e.g. coming from correlated systematic within survey, for example zero point calibration) by adding such non-block diagonal correlations to Eq. (10.42).

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Acknowledgments

This work was partially supported by travel grants by the Royal Astronom-ical Society and by the Royal Society. MCM was partially supported by a Royal Astronomical Society grant. GDS and PV were supported by a grant from the US-DOE to the CWRU theory group, and by NASA grant NNX07AG89G to GDS. PV was supported by CWRU’s College of Arts and Sciences.

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Authors and Affiliations

  1. Astrophysics Group, Imperial College, London, UK

    Marisa Cristina March

  2. The Astronomy Centre, University of Sussex, Brighton, UK

    Marisa Cristina March

  3. Theoretical Cosmology, Astrophysics Group, Dept. of Physics, Imperial College London, Blackett Laboratory, Prince Consort Rd, London, SW7 2AZ, UK

    Roberto Trotta (Lecturer)

  4. Volen Center for Complex Systems, Brandeis Univ., Waltham, USA

    Pietro Berkes (Researcher)

  5. Center for Education and Research in Cosmology and Astrophysics, Case Western Reserve Univ, Cleveland, OH, USA

    Glenn Starkman (Prof of Physics and Astronomy, and Director, Institute for the Science of Origins, and Director)

  6. Particle Physics group, Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany

    Pascal Vaudrevange (Fellow)

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  1. Marisa Cristina March
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Correspondence to Marisa Cristina March .

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    Joseph M. Hilbe

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March, M.C., Trotta, R., Berkes, P., Starkman, G., Vaudrevange, P. (2013). Improved Cosmological Constraints from a Bayesian Hierarchical Model of Supernova Type Ia Data. In: Hilbe, J. (eds) Astrostatistical Challenges for the New Astronomy. Springer Series in Astrostatistics, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3508-2_10

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