Large-Eddy Simulation (LES) is combined with advanced System Identification (SI) to simultaneously infer models for the source of combustion noise and the dynamic response to velocity fluctuations of a turbulent premixed flame. A Box-Jenkins model structure allows SI of both the noise source and the flame dynamics from time series data generated with single LES. The models that result from this ‘black-box’ SI approach are purely data-driven and do not rely on estimates of characteristic flow or flame parameters, such as turbulence intensity or flame length. In confined combustion systems the spectral distribution of combustion noise is strongly modulated by the cavity acoustics and the flame dynamics. By incorporating the identified models into a network model for the combustor acoustics, a linear Reduced Order Model (ROM) is built to predict the spectral distribution of sound pressure within the combustor for two different outlet reflection conditions. The identified flame transfer function as well as the ROM-based predictions of the pressure spectra in the combustor are compared with satisfactory qualitative and quantitative agreement against measurements. An interpretation of the pressure spectra based on eigenmode analysis elucidates the interplay between combustion noise generation, flame dynamics and cavity resonances.