Title: Inferring the parameters of a Markov process from snapshots of the steady state,
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.