  We reconstruct the expansion history of the Universe using type Ia supernovae
(SN Ia) in a manner independent of any cosmological model assumptions. To do
so, we implement a non-parametric iterative smoothing method on the Joint
Light-curve Analysis (JLA) data while exploring the SN Ia light-curve
hyper-parameter space by Monte Carlo Markov Chain sampling. We test to see how
the posteriors of these hyper-parameters depend on cosmology, whether using
different dark energy models or reconstructions shift these posteriors. Our
constraints on the SN Ia light-curve hyper-parameters from our
model-independent analysis are very consistent with the constraints from using
different parametrizations of the equation of state of dark energy, namely the
flat $\Lambda\mathrm{CDM}$ cosmology, the Chevallier-Polarski-Linder (CPL)
model, and the Phenomenologically Emergent Dark Energy (PEDE) model. This
implies that the distance moduli constructed from the JLA data are mostly
independent of the cosmological models. We also studied that the possibility
the light-curve parameters evolve with redshift and our results show
consistency with no evolution. The reconstructed expansion history of the
Universe and dark energy properties also seem to be in good agreement with the
expectations of the standard $\Lambda\mathrm{CDM}$ model. However, our results
also indicate that the data still allow for considerable flexibility in the
expansion history of the Universe.
