Inferring the parameters of a Markov process from snapshots of the steady state
This addresses a challenge in statistical physics and theoretical biology for researchers studying non-equilibrium systems, offering a novel inference approach.
The authors tackled the problem of inferring parameters of non-equilibrium Markov processes from steady-state snapshots, where traditional equilibrium methods fail, and proposed a propagator likelihood method that efficiently reconstructs parameters in systems like the asymmetric simple exclusion process and kinetic Ising model.
We seek to infer the parameters of an ergodic Markov process from samples taken independently from the steady state. Our focus is on non-equilibrium processes, where the steady state is not described by the Boltzmann measure, but is generally unknown and hard to compute, which prevents the application of established equilibrium inference methods. We propose a quantity we call propagator likelihood, which takes on the role of the likelihood in equilibrium processes. This propagator likelihood is based on fictitious transitions between those configurations of the system which occur in the samples. The propagator likelihood can be derived by minimising the relative entropy between the empirical distribution and a distribution generated by propagating the empirical distribution forward in time. Maximising the propagator likelihood leads to an efficient reconstruction of the parameters of the underlying model in different systems, both with discrete configurations and with continuous configurations. We apply the method to non-equilibrium models from statistical physics and theoretical biology, including the asymmetric simple exclusion process (ASEP), the kinetic Ising model, and replicator dynamics.