Ratio of estimated and true optical depths τ/τ₀ for 1-MBB, 2-TMPL (T_C=13 K and 17 K), and 2-MBB models. The observations consist of 160, 250, 350, and 500 μm intensities with 3% relative noise. The dots correspond to individual pixels (every 10th pixel), the solid lines show moving averages, and the shaded regions the 1-σ dispersion of the τ estimates. The χ¹ values of the ML fits (normalised by the number of fitted data points) are quoted in the frames. In frame a, observations consist of one emission component at T₁ = 15 K and one component varied in the range T₂ = 10–20 K (on x-axis), both with the same optical depth. The additional solid blue lines correspond to the 1-σ error estimates from the MCMC fit of the 2-TMPL model. In frame b, the observations correspond to a continuous temperature distribution, T ~ N(〈T〉, σ_T). The x-axis shows the 〈T〉 value, with σ_T = 1 K for the first and σ_T = 5 K for the second half. Frame c is the same as frame b but the SED fits assuming β = 1.7 instead of the correct value of β = 1.9.