On a framework of data assimilation for neuronal networks

Both results the paper claims (consistency of the hyperparameter MLE under R1–R4 and Hellinger–Lipschitz well-posedness of the posterior) are plausible and standard, but the paper’s proofs omit critical steps. In Theorem 1, the argument mixes limits in n and m, invokes WLLN with a vanishing (in m) mean without a diagonal/iterated limit, and applies Slutsky to a ratio whose denominator still depends on the unknown estimator; no localization/strong-convexity argument is given to ensure the optimizer lies near the truth. In Theorem 2, the proof drops model terms, assumes bounded densities, and never establishes a uniform lower bound on the evidence Z(y), which is necessary for the Hellinger bound. The candidate solution fills these gaps with standard, correct arguments (Hessian positivity near the truth; gradient control via Hellinger; explicit O_p(n^{-1/2})+O(ε(m)) rate; and a classical Z(y) lower bound via Markov and an integrability assumption).