Parameter Inference and Nonequilibrium Identification for Markov Networks Based on Coarse-Grained Observations.

Most experiments can only detect a set of coarse-grained clusters of a molecular system, while the internal microstates are often inaccessible. Here, based on an infinitely long coarse-grained trajectory, we obtain a set of sufficient statistics that extracts all statistic information of coarse-grained observations. Based on these sufficient statistics, we set up a theoretical framework of parameter inference and nonequilibrium identification for a general Markov network with an arbitrary number of microstates and arbitrary coarse-grained partitioning. Our framework can be used to identify whether the sufficient statistics are enough for empirical estimation of all unknown parameters and we can also provide a quantitative criterion that reveals nonequilibrium. Our nonequilibrium criterion generalizes the one obtained [J. Chem. Phys. 132, 041102 (2010)JCPSA60021-960610.1063/1.3294567] for a three-state system with two coarse-grained clusters and is capable of detecting a larger nonequilibrium region compared to the classical criterion based on autocorrelation functions.