Comparison of the reference likelihood function with two approximations that neglect and account for correlations. The 1σ, 2σ, and 3σ areas of the reference likelihood function in the HR diagram are shown by the shaded areas. The red contours show the same confidence levels of a likelihood model that neglects the correlation in luminosity and effective temperature, and the black contours show our new likelihood model for a correlation parameter of ϕ = 3.916 × 10^-5 K^-1. The marginalised observables are T_eff = 24 700 ± 2000 K and log L/L_⊙ = 4.410 ± 0.084 for all three likelihood models.