MCMC sampling of the χ² statistic for the global fit, showing posterior distributions of selected parameters. Shown are the candle parameters α₀, β, and α_M for RRab and RRc stars. The corresponding parameters for T2Cep exhibit similar distributions and are omitted here for clarity. The plot also includes one representative host distance and one anchor correction factor. Posterior distributions (black) are well approximated by Gaussians, with means and dispersions closely matching the least-squares solution from the baseline (red). Contours indicate the 1σ, 2σ, and 3σ confidence regions. Correlations between period slopes and metallicity terms are discussed further in Sect. 4.2.2.