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We present a systematic first-principles modelling study of the structural dynamics and thermal transport in the CoSb3 skutterudites with a series of noble-gas filler atoms. Filling with chemically-inert atoms provides an idealised model for isolating the effects of the fillers from the impact of redox changes to the host electronic structure. A range of analysis techniques are proposed to estimate the filler rattling frequencies, to quantify the separate impacts of the filler on the phonon group velocities and lifetimes, and to show ho