We propose a novel molecular computing scheme for statistical inference. We\nfocus on the much-studied statistical inference problem of computing maximum\nlikelihood estimators for log-linear models. Our scheme takes log-linear models\nto reaction systems, and the observed data to initial conditions, so that the\ncorresponding equilibrium of each reaction system encodes the corresponding\nmaximum likelihood estimator. The main idea is to exploit the coincidence\nbetween thermodynamic entropy and statistical entropy. We map a Maximum Entropy\ncharacterization of the maximum likelihood estimator onto a Maximum Entropy\ncharacterization of the equilibrium concentrations for the reaction system.\nThis allows for an efficient encoding of the problem, and reveals that reaction\nnetworks are superbly suited to statistical inference tasks. Such a scheme may\nalso provide a template to understanding how in vivo biochemical signaling\npathways integrate extensive information about their environment and history.\n