Probabilistic predictions of SIS epidemics on networks based on population-level observations

The paper sets up the BD master equation (1), the parametric birth-rate model (2), and the Bayesian pushforward m_k with equal-tailed predictive intervals Q(x) (6–9), and distinguishes these from MAP-based intervals (12), but it does not provide formal proofs for probability conservation, posterior-predictive identification, asymptotic concentration, model selection consistency, or robustness; those are treated empirically. The candidate solution supplies standard, largely correct arguments for A–E, aligning with the paper’s definitions and qualitative findings (e.g., that MAP intervals reflect intrinsic randomness only and are narrower) while adding missing theoretical justifications. Minor caveats: at k=0 the boundary is absorbing rather than reflecting, and the robustness bound’s matrix-norm choice needs a small clarification. Overall, the model solution is correct; the paper is accurate but theoretically incomplete on these points (cf. eqs. (1), (2), (6)–(9), (12), and the discussion of applicability for 50 ≤ k ≤ 950 and the empirical narrowing of differences with longer observation windows).