Dr. Carlo Albert, EAWAG, Switzerland

Bayesian Inference for Stochastic Differential Equation Models through Hamiltonian Scale Separation

Bayesian parameter inference is a fundamental problem in model-based data science. Given observed data, which is believed to be a realization of some parameterized model, the aim is to find a distribution of likely parameter values that are able to explain the observed data. This so-called posterior distribution expresses the probability of a given parameter to be the "true" one, and can be used for making probabilistic predictions. For truly stochastic models this posterior distribution is typically extremely expensive to evaluate. We propose a novel approach for generating posterior parameter distributions, for stochastic differential equation models calibrated to measured time-series. The algorithm is inspired by re-interpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, whose dynamics is confined by both the model and the measurements. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for 1D problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.