Accounting for motion of supernova host galaxy in statistical inference from SNIa data

We introduce a Bayesian method to estimate peculiar velocities of Type Ia supernova (SNIa) host galaxies by employing the magnitude-redshift relationship of SNIa. Random peculiar motions act as noise in the estimation of redshift, and constitute independent variables in the SNIa data. We develop a method to take into account errors in independent variables for general nonlinear models. Using the MCMC sampling technique, we implement numerical codes to estimate peculiar velocities along with other cosmological parameters. In this paper, we study the impact of these velocities on cosmological parameters by treating them as nuisance parameters. We apply our proposed method on the Pantheon sample of SNIa and show a few percent shift on the central values of inferred cosmological parameters. Although the current data are not particularly sensitive to this error, using simulated data, we also gauge the efficacy of our method on the future SNIa observations and show that future data require the inclusion of this error in cosmological parameter estimation. Our method complements several existing methods that seek to estimate peculiar velocities using galaxy data and N-body simulations and extends to higher redshifts.