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We introduce a new method to propagate uncertainties in the beam shapes usedto measure the cosmic microwave background to cosmological parametersdetermined from those measurements. The method, which we call Markov Chain BeamRandomization, MCBR, randomly samples from a set of templates or functions thatdescribe the beam uncertainties. The method is much faster than directnumerical integration over systematic `nuisance' parameters, and is notrestricted to simple, idealized cases as is analytic marginalization. It doesnot assume the data are normally distributed, and does not require Gaussianpriors on the specific systematic uncertainties. We show that MCBR properlyaccounts for and provides the marginalized errors of the parameters. The methodcan be generalized and used to propagate any systematic uncertainties for whicha set of templates is available. We apply the method to the Planck satellite,and consider future experiments. Beam measurement errors should have a smalleffect on cosmological parameters as long as the beam fitting is performedafter removal of 1/f noise.

Markov Chain Beam Randomization: a study of the impact of PLANCK beam measurement errors on cosmological parameter estimation