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Application of Bayesian graphs to SN Ia data analysis and compression
Ma, Cong; Corasaniti, Pier-Stefano; Bassett, Bruce A.
AA(Purple Mountain Observatory, Chinese Academy of Sciences, 2 West Beijing Rd, 210008 Nanjing, China; Graduate School, University of the Chinese Academy of Sciences, 19A Yuquan Rd, 100049 Beijing, China; LUTH, UMR 8102 CNRS, Observatoire de Paris, PSL Research University, Université Paris Diderot, 5 Place Jules Janssen, F-92190 Meudon, France ), AB(LUTH, UMR 8102 CNRS, Observatoire de Paris, PSL Research University, Université Paris Diderot, 5 Place Jules Janssen, F-92190 Meudon, France), AC(Department of Mathematics and Applied Mathematics, University of Cape Town, Cross Campus Rd, Rondebosch 7700, South Africa; African Institute for Mathematical Sciences, 6-8 Melrose Rd, Muizenberg 7945, South Africa; South African Astronomical Observatory, Observatory Rd, Observatory 7925, South Africa)
Monthly Notices of the Royal Astronomical Society, Volume 463, Issue 2, p.1651-1665 (MNRAS Homepage)
Publication Date:
Astronomy Keywords:
cosmological parameters, distance scale, methods: data analysis, methods: statistical, supernovae: general, cosmolo-gical parameters
Abstract Copyright:
2016 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society
Bibliographic Code:


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 chi2 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 chi2 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 6sigma shift of the SN light-curve colour correction. In addition, we find that the evidence for a host galaxy correction is now only 2.4sigma. Systematic offsets on the cosmological parameters remain small, but may increase by combining constraints from complementary cosmological probes. The bias of the chi2 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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