
{\bf  Best fit parameters obtained using Julia's Turing.jl Bayesian inference}. Here $p_{\Lambda} \equiv 1 - p_k - p_m - p_r$; $p_5 = w$ in the $w$CDM,  $(p_5, p_6)$ are $(\omega_0, \omega_a)$, $(A_s, \alpha)$, $(\omega_x, \delta)$ and $(\omega_0, \Omega_e)$ in the CPL, GCG, IDE and EDE models, respectively; the EDEP model extra parameters are $(p_5, p_6,p_7) = (p_a,w_n,Z^c)$; $ \sigma^2$ means residuals. In the GCG model $p_m$ was substituted by the present density parameter of baryonic matter $p_b = \Omega_b = 0.0451$, according to the WMAP 7yr results \cite{Komatsu2011} following the example in  \cite{shi2012}.	
