Parameter inference and nonequilibrium identification for Markovian systems based on coarse-grained observations

TL;DR

This paper develops a theoretical framework for parameter inference and nonequilibrium detection in Markovian systems using coarse-grained observations, enabling analysis of systems with inaccessible microstates.

Contribution

It introduces a set of sufficient statistics for coarse-grained data and a generalized nonequilibrium criterion applicable to complex Markovian systems.

Findings

Framework can identify when sufficient statistics are adequate for parameter estimation.

Provides a quantitative criterion for detecting nonequilibrium states.

Generalizes previous criteria to larger nonequilibrium regions.

Abstract

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 which 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 Markovian system with an arbitrary number of microstates and arbitrary coarse-grained partitioning. Our framework can 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)] 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.