Data-driven coarse graining in action: Modelling and prediction of complex systems

In many natural, technological, social and economic applications, one is commonly faced with the task of estimating statistical properties from empirical data (experimental observations), such as mean-first-passage times of a temporal continuous process. Typically, however, an accurate and reliable estimation of such properties directly from the data alone is not possible as the time series is often too short, or the particular phenomenon of interest is only observed rarely. We propose here a theoretical-computational framework which enables the systematic and rational estimation of statistical quantities of a given temporal process, such as waiting times between subsequent bursts of activity. Our framework is illustrated with applications from real-world data sets, ranging from marine biology to climate change.