Before revision: We propose a scheme for computing Maximum Likelihood Estimators for Log-Linear modelsusing reaction networks, and prove its correctness. Our scheme exploits the toric structure of equilibrium points of reaction networks .
After revision: We propose a novel molecular computing scheme for statistical inference. We focus on the much-studied statistical inference problem of computing maximum likelihood estimators for log-linear models. Our scheme takes log-linear models to reaction systems, and the observed data to initial conditions, so that the corresponding equilibrium of each reaction system encodes the corresponding maximum likelihood estimator. The main idea is to exploit the coincidence between thermodynamic entropy and statistical entropy. We map a Maximum Entropy characterization of the maximum likelihood estimator onto a Maximum Entropy characterization of the equilibrium concentrations for the reaction system .