Inferring the parameters of a Markov process from snapshots of the steady state

TL;DR

This paper introduces a new method called propagator likelihood for inferring parameters of non-equilibrium Markov processes from steady-state samples, overcoming limitations of equilibrium-based methods.

Contribution

It proposes the propagator likelihood as a novel inference tool for non-equilibrium steady states, applicable to both discrete and continuous systems.

Findings

Effective reconstruction of model parameters in various non-equilibrium systems

Applicable to both discrete and continuous configuration spaces

Demonstrated on models like ASEP, kinetic Ising, and replicator dynamics

Abstract

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.