Steve: A Hierarchical Bayesian Model for Supernova Cosmology

We present a new Bayesian hierarchical model (BHM) named Steve for performing type Ia supernova (SN Ia) cosmology fits. This advances previous works by including an improved treatment of Malmquist bias, accounting for additional sources of systematic uncertainty, and increasing numerical efficiency. Given light curve fit parameters, redshifts, and host-galaxy masses, we fit Steve simultaneously for parameters describing cosmology, SN Ia populations, and systematic uncertainties. Selection effects are characterised using Monte-Carlo simulations. We demonstrate its implementation by fitting realisations of SN Ia datasets where the SN Ia model closely follows that used in Steve . Next, we validate on more realistic SNANA simulations of SN Ia samples from the Dark Energy Survey and low-redshift surveys (DES Collaboration 2018). These simulated datasets contain more than $60\,000$ SNe Ia, which we use to evaluate biases in the recovery of cosmological parameters, specifically the equation-of-state of dark energy, $w$. This is the most rigorous test of a BHM method applied to SN Ia cosmology fitting, and reveals small $w$-biases that depend on the simulated SN Ia properties, in particular the intrinsic SN Ia scatter model. This $w$-bias is less than $0.03$ on average, less than half the statistical uncertainty on $w$. These simulation test results are a concern for BHM cosmology fitting applications on large upcoming surveys, and therefore future development will focus on minimising the sensitivity of Steve to the SN Ia intrinsic scatter model.