An accurate description of the chemical processes involved in the oxidation of hydrocarbons may include hundreds of reactions and fifty or more chemical species. Kinetics models of these chemical mechanisms are often embedded in a fluid dynamics solver to represent combustion. Because the computational cost of such detailed mechanisms is so high, it is common practice to use drastically reduced mechanisms. But, this introduces modeling errors which may render the model inadequate. In this work, the goal is to account for the discrepancy between the detailed model and its reduced version by incorporating an inadequacy operator that is both stochastic and physically meaningful. The bulk of the operator is described by a random matrix, which displays interesting properties due to conservation constraints. The parameters of the operator are characterized by probability distributions, which are calibrated using high-dimensional hierarchical Bayesian modeling. In particular, we investigate how the inclusion of the inadequacy operator affects the prediction of a quantity of interest, namely, the flame speed of a one-dimensional hydrogen laminar flame.