Markov chain beam randomization: a study of the impact of PLANCK beam measurement errors on cosmological parameter estimation

G. Rocha^1,2, L. Pagano³, K. M. Górski^1,2,4, K. M. Huffenberger⁵, C. R. Lawrence¹ and A. E. Lange²

¹ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena CA 91109, USA
² California Institute of Technology, Pasadena CA 91125, USA
³ Physics Department and sezione INFN, University of Rome “La Sapienza”, Ple Aldo Moro 2, 00185 Rome, Italy
⁴ Warsaw University Observatory, Aleje Ujazdowskie 4, 00478 Warszawa, Poland
⁵ Department of Physics, University of Miami, 1320 Campo Sano Avenue, Coral Gables, FL 33124, USA

Received: 31 July 2009
Accepted: 13 January 2010

Abstract

We introduce a new method to propagate uncertainties in the beam shapes used to measure the cosmic microwave background to cosmological parameters determined from those measurements. The method, called markov chain beam randomization (MCBR), randomly samples from a set of templates or functions that describe the beam uncertainties. The method is much faster than direct numerical integration over systematic “nuisance” parameters, and is not restricted to simple, idealized cases as is analytic marginalization. It does not assume the data are normally distributed, and does not require Gaussian priors on the specific systematic uncertainties. We show that MCBR properly accounts for and provides the marginalized errors of the parameters. The method can be generalized and used to propagate any systematic uncertainties for which a set of templates is available. We apply the method to the Planck satellite, and consider future experiments. Beam measurement errors should have a small effect on cosmological parameters as long as the beam fitting is performed after removal of 1/f noise.