Extracting Signal out of Chaos: Advancements on MAGI for Bayesian Analysis of Dynamical Systems

The paper defines the Bayesian stability-probability estimator as a posterior expectation approximated by the Monte Carlo average of an indicator over HMC draws and uses it for empirical analysis, but it does not provide theoretical guarantees such as unbiasedness, variance, SLLN convergence, or a non-asymptotic misclassification bound; the construction appears only as a proof-of-concept with experiments (see the estimator in Chapter 6 and its use in figures and discussion ). The model’s solution correctly supplies these missing properties under standard assumptions (i.i.d. posterior draws or, more generally, stationarity for unbiasedness; Hoeffding concentration under independence). The paper’s reliance on HMC sampling is consistent with the model’s setup, but the paper neither states independence nor provides effective-sample-size caveats (background on HMC sampling within MAGI/pMAGI is given earlier in the manuscript ).