Non-asymptotic confidence regions for the parameters of dynamical systems

In this seminar we consider the problem of constructing confidence regions for the model parameters of dynamical systems from observed data. Taking a major departure from previous methods, we introduce a new approach called Leave-out Sign-dominant Correlation Regions (LSCR) which delivers confidence regions with guaranteed probability. Based on subsampling techniques, we derive the exact probability that the true parameters belong to certain regions in the parameter space. By intersecting these regions, a confidence set containing the true parameters with guaranteed probability is obtained. All results hold true for any finite number of data point. Moreover, prior knowledge on the noise affecting the data is reduced to a minimum. The approach will be illustrated on simulation examples, showing that it delivers practically useful confidence sets with guaranteed probabilities.