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Article Dans Une Revue Monthly Notices of the Royal Astronomical Society Année : 2016

Application of Bayesian graphs to SN Ia data analysis and compression

Résumé

Bayesian graphical models are an efficient tool for modelling complex data and derive self-consistent expressions of the posterior distribution of model parameters. We apply Bayesian graphs to perform statistical analyses of Type Ia supernova (SN Ia) luminosity distance measurements from the joint light-curve analysis (JLA) data set. In contrast to the χ 2 approach used in previous studies, the Bayesian inference allows us to fully account for the standard-candle parameter dependence of the data covariance matrix. Comparing with χ 2 analysis results , we find a systematic offset of the marginal model parameter bounds. We demonstrate that the bias is statistically significant in the case of the SN Ia standardization parameters with a maximal 6σ shift of the SN light-curve colour correction. In addition, we find that the evidence for a host galaxy correction is now only 2.4σ. Systematic offsets on the cosmological parameters remain small, but may increase by combining constraints from complementary cosmological probes. The bias of the χ 2 analysis is due to neglecting the parameter-dependent log-determinant of the data covariance, which gives more statistical weight to larger values of the standardization parameters. We find a similar effect on compressed distance modulus data. To this end, we implement a fully consistent compression method of the JLA data set that uses a Gaussian approximation of the posterior distribution for fast generation of compressed data. Overall, the results of our analysis emphasize the need for a fully consistent Bayesian statistical approach in the analysis of future large SN Ia data sets.
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Dates et versions

hal-02337433 , version 1 (31-01-2020)

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Cong Ma, Pier-Stefano Corasaniti, Bruce Bassett. Application of Bayesian graphs to SN Ia data analysis and compression. Monthly Notices of the Royal Astronomical Society, 2016, 463 (2), pp.1651-1665. ⟨10.1093/mnras/stw2069⟩. ⟨hal-02337433⟩
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