Discrete state models are a common tool of modeling in many areas. E.g., Markov state models as a particular representative of this model family became one of the major instruments for analysis and understanding of processes in molecular dynamics (MD). Here we extend the scope of discrete state models to the case of systematically missing scales, resulting in a nonstationary and nonhomogeneous formulation of the inference problem. We demonstrate how the recently developed tools of nonstationary data analysis and information theory can be used to identify the simultaneously most optimal (in terms of describing the given data) and most simple (in terms of complexity and causality) discrete state models. We apply the resulting formalism to a problem from molecular dynamics and show how the results can be used to understand the spatial and temporal causality information beyond the usual assumptions. We demonstrate that the most optimal explanation for the appropriately discretized/coarse-grained MD torsion angles data in a polypeptide is given by the causality that is localized both in time and in space, opening new possibilities for deploying percolation theory and stochastic subgridscale modeling approaches in the area of MD.
Keywords: Granger causality; multiscale systems; nonstationarity; probabilistic networks; regularization.