Flowchart of the iterative procedure for parameter estimation in the Bayesian ensemble EPM fit. At each step, we sample a new set of parameters, including the Hubble constant H₀, unexplained dispersion σ_int, and the peculiar velocity v_pec and time of explosion t₀ for each SN, from the priors. The priors are visually indicated above each parameter. From the parameters, we then calculate true cosmological redshifts z_cosmo and luminosity distances D_L, ending with the computation of the proposed θ/v_ph^pred vectors using the referenced equations. The process concludes with the comparison of the proposed and measured θ/v_ph vectors, evaluating the likelihood for the proposed σ_int. This cycle repeats for each new set of parameters, slowly building up the posterior distribution.