Application of Bayesian graphs to SN Ia data analysis and compression

TL;DR

This paper demonstrates that Bayesian graphical models provide a more accurate analysis of Type Ia supernova data than traditional methods, revealing significant biases in standardization parameters and emphasizing the importance of Bayesian approaches for future cosmological studies.

Contribution

The paper introduces a Bayesian graphical model approach for SN Ia data analysis, highlighting its advantages over traditional $$ methods and providing a new data compression technique.

Findings

Bayesian analysis reveals a 6 sigma shift in SN light-curve color correction.

Evidence for host galaxy correction is only 2.4 sigma.

Biases in standard $$ analysis stem from neglecting parameter-dependent data covariance.

Abstract

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 $\chi^2$ 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 $\chi^2$ 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 6 $\sigma$ shift of the SN light-curve colour correction. In addition, we find that the evidence for a host galaxy correction is now only 2.4 $\sigma$. Systematic offsets on the cosmological parameters remain small, but may increase by combining constraints from complementary cosmological probes. The bias of the $\chi^2$ 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.