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

In many physical, technological, social, and economic applications, one is commonly faced with the task of estimating statistical properties, such as mean first passage times of a temporal continuous process, from empirical data (experimental observations). 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 rarely observed. We propose here a theoretical-computational framework which provides us with a systematic and rational estimation of statistical quantities of a given temporal process, such as waiting times between subsequent bursts of activity in intermittent signals. Our framework is illustrated with applications from real-world data sets, ranging from marine biology to paleoclimatic data.