On the abrupt change of the maximum likelihood state in a simplified stochastic thermohaline circulation system

The paper defines the bridge maximum-likelihood state ψ(t) via the product identity p(y3,T|y,t)·p(y,t|y1,0) and computes it by solving the forward/backward Fokker–Planck equations, reporting a clear jump and, crucially, that stronger noise (ε=0.25 vs 0.20) yields an earlier jump time (≈6.32 vs ≈6.86) for T=10 and F̄=1.1, μ2=6.2, with equilibria y1≈0.2402, y2≈0.6911, y3≈1.0687 . The candidate solution uses the same identity and a similar PDE approach but produces substantially different jump times (≈5.25 and ≈5.37) and the opposite monotonic trend (claiming larger ε delays the jump). The candidate’s qualitative “existence” argument is also incomplete (it does not rule out a global maximizer outside the chosen neighborhoods), whereas the paper’s result is internally consistent with its stated method and parameters. Therefore, on reconciliation, the paper’s claims are supported by its computations, but the model’s numerical conclusions and ε-dependence are incorrect for the stated setup.