Accurate predictions of soot emissions from combustion systems are required to implement the design of low-emission aero-engine combustors that can mitigate the effects of particulate matter on human health and the environment. The use of detailed models of soot formation can be unfeasible in terms of computational costs for optimisation procedures involving a large number of numerical simulations of different combustor configurations. A reduced-order formulation for turbulence-chemistry interactions and kinetic post-processing of Computational Fluid Dynamics (CFD) simulations, i.e., the Incompletely Stirred Reactors Network (ISRN) method, has recently provided promising qualitative predictions of soot emissions while allowing the use of complex chemistry at minimal computational costs. However, loss of accuracy and uncertainty in the predictions of relevant quantities, e.g., temperature and pollutant emissions, should be accounted for when reduced-order models like the ISRN method are employed. Hence, the integration of the ISRN method with data-driven approaches included in the framework of Uncertainty Quantification (UQ) has been pursued and is presented in this work. The grid parameters of the ISRN were calibrated via a UQ approach so that the predictions of temperature within an aero-engine model combustor match those obtained by a detailed CFD simulation with accuracy higher than 90%. The UQ approach results in the determination of a feasible set of grid parameters and information about the correlation between them. Then, the proposed methodology has been applied on soot emissions in the aero-engine combustor to obtain bounded predictions from the ISRN method that are of the same order of magnitude as the corresponding ones provided by the high-order Conditional Moment Closure (CMC) combustion model.