Prior 𝒫(ω) (yellow) and posterior $\mathcal{P}(\mathit{\omega }|{\stackrel{\mathbf{\sim }}{\mathit{\omega }}}_{\mathrm{O}})$ distributions of (Ω_m,  Ω_b,  σ₈,  n_S), estimated using Population Monte Carlo based on the Fisher-Rao distance $d_{\mathrm{FR}}(\stackrel{\mathbf{\sim }}{\mathit{\omega }},{\stackrel{\mathbf{\sim }}{\mathit{\omega }}}_{\mathrm{O}})$ between simulated and observed summaries. The posterior with the well-specified Model A is represented by the green contours, whilst the red contours show the results with the misspecified Model B, both depicting the 1σ and 2σ credible regions. The percent-level misspecification in Model B introduces a bias exceeding 2σ in the (Ω_m, σ₈) plane. The one-dimensional marginal posterior distributions of the parameters are displayed on the diagonal, following the same colour scheme. The dashed line indicates the ground truth parameters ω_gt.