  Many biological systems can be modeled as a chemical reaction network with
unknown parameters. Data available to identify these parameters are often in
the form of a stationary distribution, such as that obtained from measurements
of a cell population. In this work, we introduce a framework for analyzing the
identifiability of the reaction rate coefficients of chemical reaction networks
from stationary distribution data. Working with the linear noise approximation,
which is a diffusive approximation to the chemical master equation, we give a
computational procedure to certify global identifiability based on Hilbert's
Nullstellensatz. We present a variety of examples that show the applicability
of our method to chemical reaction networks of interest in systems and
synthetic biology, including discrimination between possible molecular
mechanisms for the interaction between biochemical species.
