In this talk, I will present a calculation of the inclusive jet transverse momentum spectrum at the LHC performed at next-to-next-to-leading order, including resummation of logarithms of the jet radius R at next-to-next-to-leading-logarithmic accuracy. Inclusive jet production is a key process for fitting parton distribution functions, which makes an accurate understanding of the uncertainties on the theory predictions particularly important. However, estimates of missing-higher-order uncertainties obtained from scale variations are notoriously unreliable for this process. Considerably more robust theory uncertainties can be obtained using the method of theory nuisance parameters. I will present how this method can be applied to inclusive jet production and demonstrate that the uncertainties obtained this way are far more consistent than the scale uncertainties.