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 characterized using Monte Carlo simulations. We demonstrate its implementation by fitting realizations of SN Ia data sets 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 et al. 2018). These simulated data sets 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; therefore, future development will focus on minimizing the sensitivity of Steve to the SN Ia intrinsic scatter model. ; The DES data management system is supported by the National Science Foundation under grant Nos. AST-1138766 and AST-1536171. The DES participants from Spanish institutions are partially supported by MINECO under grants AYA2015-71825, ESP2015-66861, FPA2015-68048, SEV2016-0588, SEV-2016-0597, and MDM-2015-0509, some of which include ERDF funds from the European Union. IFAE is partially funded by the CERCA program of the Generalitat de Catalunya. Research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Program (FP7/2007- 2013), including ERC grant agreements 240672, 291329, and 306478. We acknowledge support from the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO) through project No. CE110001020 and the Brazilian Instituto Nacional de Ciência e Tecnologia (INCT) e-Universe (CNPq grant 465376/2014-2). This manuscript has been authored by the Fermi Research Alliance, LLC, under contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes