This work concerns the uncertainties arising from the derivation of global chemistry models and their impact on the predictions using modern combustion simulations. We perform the inference of the parameters of a two-step reaction mechanism for CH 4 , using synthetic observations of one-dimensional laminar flames generated using detailed mechanism simulations. Introduction of Principal Component Analysis (PCA) and the Polynomial Chaos (PC) expansion, to approximate the global model predictions, enables a full assessment of the inferred global model's posterior. In particular, we employ the Bayesian posteriors' extensive sampling to estimate mean, Maximum a Posteriori, and confidence intervals of the inferred global model's predictions. We contrast the posterior distributions of global quantities of the flame, namely the laminar flame speed, the thermal flame thickness, and the reaction zone thickness, depending on the inference's observations. Finally, we propagate the global chemistry model's posterior distribution through two-dimensional direct numerical simulations (DNS) of a flame-vortex interaction problem. This study highlights the importance of quantifying posterior uncertainties to fully appreciate the impact of using a global model in real-world reactive simulations.