Theoretically predicted rate coefficient parameters play an increasing role in combustion kinetic models. Understanding the uncertainty propagation during RRKM/master equation modeling and quantitatively evaluating the uncertainties of the phenomenological rate coefficients would be a great boon to chemical modeling. In the present work, the global uncertainty and sensitivity analysis were performed for a prototypical multiwell and multichannel reaction system (on the C4H7 potential energy surface) over the temperature and pressure range of 300-2300 K and 0.01-100 atm. Six reactions including chemical activation reactions and unimolecular reactions were studied, focusing on the uncertainty of both absolute rate coefficients and their branching ratios. To reveal the nature of uncertainty propagation from input parameters at different theoretical levels, five scenarios were designed to mimic the uncertainty from high-, moderate- and low- levels of theories. For absolute rate coefficients, the temperature dependence of uncertainties for all the reactions is found to be much stronger than the pressure dependence. The pressure dependence is mainly determined by the reaction type (chemical activation or thermal dissociation, directly-connected or well-skipping). For the branching ratio, sensitivity analysis shows that the input parameters that are very important in determining the absolute rate coefficients do not necessarily have high sensitivity coefficients in predicting the branching ratio. As a consequence, the uncertainty of the theoretically calculated branching ratio can be smaller than that of the rate coefficients. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.