Detecting hidden states in stochastic dynamical systems

Inferring the number of states of a stochastic system from partial measurements is a fundamental problem in physics, for which methodological tools remain scarce. It is sometimes difficult to distinguish the stochastic dynamical states from measurements, deceiving us into incorrect models and flawed understanding of natural phenomena. Here, we propose a model-free statistical framework, grounded in network and control theory, to estimate the number of states of a stochastic system from perceptible dynamics. The framework extends previous techniques for deterministic systems, based on the rank of ancillary matrices. We show applications of our approach to a variety of physics domains, such as statistical mechanics, biophysics, physical chemistry, and epidemiology.