Spectral-shape posterior for a simulated steep-spectrum source (α = −0.7, β = −0.3, γ = 0.0). Left: noisy observed spectrum (gray), true model (red), and 80 posterior-predictive draws (blue). Right: marginal and joint posteriors for α, β, and γ; contours enclose 68% and 95% credible regions, and red dashed lines mark the injected truth.