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Inference on unknown quantities in dynamical systems via observational datais essential for providing meaningful insight, furnishing accurate predictions,enabling robust control, and establishing appropriate designs for futureexperiments. Merging mathematical theory with empirical measurements in astatistically coherent way is critical and challenges abound, e.g.,:ill-posedness of the parameter estimation problem, proper regularization andincorporation of prior knowledge, and computational limitations on fulluncertainty qualification. To address these issues, we propose a new method forlearning parameterized dynamical systems from data. In many ways, our proposalturns the canonical framework on its head. We first fit a surrogate stochasticprocess to observational data, enforcing prior knowledge (e.g., smoothness),and coping with challenging data features like heteroskedasticity, heavy tailsand censoring. Then, samples of the stochastic process are used as "surrogatedata" and point estimates are computed via ordinary point estimation methods ina modular fashion. An attractive feature of this approach is that it is fullyBayesian and simultaneously parallelizable. We demonstrate the advantages ofour new approach on a predator prey simulation study and on a real worldapplication involving within-host influenza virus infection data paired with aviral kinetic model.

Parameter and Uncertainty Estimation for Dynamical Systems Using Surrogate Stochastic Processes