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Three parameter estimation methods are compared for the discrimination between two kinetic models of methanol and DME synthesis over Cu/ZnO/Al2O3 catalysts. Two methods apply Bayes’ rule and Monte Carlo sampling to approximate the posterior distribution, while the third one is the popular frequentist method of finding a maximum likelihood estimate and constructing ellipsoidal confidence regions. The credible regions obtained with either Bayesian methods are similar, and they are consistently smaller and more informative than the frequentist confidence regions. Both kinetic models suffer from some practical identifiability issues for the experimental data at hand, but the evidence derived from the Bayesian estimation strongly favors the kinetic model that accounts for direct CO hydrogenation.