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Parameter inference is a fundamental problem in data-driven modeling. Givenobserved data that is believed to be a realization of some parameterized model,the aim is to find parameter values that are able to explain the observed data.In many situations, the dominant sources of uncertainty must be included intothe model, for making reliable predictions. This naturally leads to stochasticmodels. Stochastic models render parameter inference much harder, as the aimthen is to find a distribution of likely parameter values. In Bayesianstatistics, which is a consistent framework for data-driven learning, thisso-called posterior distribution can be used to make probabilistic predictions.We propose a novel, exact and very efficient approach for generating posteriorparameter distributions, for stochastic differential equation models calibratedto measured time-series. The algorithm is inspired by re-interpreting theposterior distribution as a statistical mechanics partition function of anobject akin to a polymer, where the measurements are mapped on heavier beadscompared to those of the simulated data. To arrive at distribution samples, weemploy a Hamiltonian Monte Carlo approach combined with a multiple time-scaleintegration. A separation of time scales naturally arises if either the numberof measurement points or the number of simulation points becomes large.Furthermore, at least for 1D problems, we can decouple the harmonic modesbetween measurement points and solve the fastest part of their dynamicsanalytically. Our approach is applicable to a wide range of inference problemsand is highly parallelizable.

Boosting Bayesian Parameter Inference of Nonlinear Stochastic Differential Equation Models by Hamiltonian Scale Separation