  We study the simplifications occurring in any likelihood function in the
presence of a large number of small systematic uncertainties. We find that the
marginalisation of these uncertainties can be done analytically by means of
second-order error propagation, error combination, the Lyapunov central limit
theorem, and under mild approximations which are typically satisfied for LHC
likelihoods. The outcomes of this analysis are i) a very light treatment of
systematic uncertainties ii) a convenient way of reporting the main effects of
systematic uncertainties such as the detector effects occuring in LHC
measurements.
