A Bayesian estimator for non-linear regression with errors in variables in cosmology

Ujjwal Kumar Upadhyay, Tarun Deep Saini

While fitting a non-linear model to data, it is common to consider errors only in the dependent variable and treat other variables as perfectly measured. A more flexible model fitting considering errors in independent variables is expected to better estimate the parameters of the model from the same data. We propose a Bayesian estimator to fit non-linear errors-in-variables models and employ it to study the effect of considering redshift errors on the cosmological parameter estimation from redshift-magnitude data of Type Ia supernovae. We find that the Pantheon data favors a lower value of the Hubble constant and a slightly higher value of the matter density parameter for the ΛCDM model compared to the values obtained from standard fitting method ignoring redshift errors.