Title: Inference in the Duffing system with a sequential ABC-UKF algorithm
Authors: Michela Eugenia Pasetto - University of Bologna (Italy) [presenting]
Umberto Noe - University of Glasgow (United Kingdom)
Alessandra Luati - University of Bologna (Italy)
Dirk Husmeier - Biomathematics and Statistics Scotland, Edinburgh (UK)
Abstract: An algorithm is developed to infer the parameters of a nonlinear chaotic system of differential equations (Duffing oscillator) based on the Unscented Kalman Filter (UKF). We have found that the overall inference performance of the UKF and its convergence critically depend on the location of the so-called sigma points and the initialization of the algorithm. To address these limitations, we propose a novel algorithm called Sequential ABC-UKF. First, we apply Approximate Bayesian Computation (ABC) with Sequential Monte Carlo (SMC) to provide a starting value in parameter space for informed initialization of the UKF. Second, we optimize the sigma point locations, comparing two alternative schemes: Bayesian optimization versus exhaustive discrete grid search. We demonstrate the effectiveness of the proposed method with a simulation study and real data analysis.