  Measurement of Cosmic Microwave Background (CMB) anisotropies has been
playing a lead role in precision cosmology by providing some of the tightest
constrains on cosmological models and parameters. However, precision can only
be meaningful when all major systematic effects are taken into account.
Non-circular beams in CMB experiments can cause large systematic deviation in
the angular power spectrum, not only by modifying the measurement at a given
multipole, but also introducing coupling between different multipoles through a
deterministic bias matrix. Here we add a mechanism for emulating the effect of
a full bias matrix to the Planck likelihood code through the parameter
estimation code SCoPE. We show that if the angular power spectrum was measured
with a non-circular beam, the assumption of circular Gaussian beam or
considering only the diagonal part of the bias matrix can lead to huge error in
parameter estimation. We demonstrate that, at least for elliptical Gaussian
beams, use of scalar beam window functions obtained via Monte Carlo simulations
starting from a fiducial spectrum, as implemented in Planck analyses for
example, leads to em only few percent of sigma deviation of the best-fit
parameters. However, we notice more significant differences in the posterior
distributions for some of the parameters, which would in turn lead to incorrect
errorbars. These differences can be reduced, so that the errorbars match within
few percent, by adding an iterative reanalysis step, where the beam window
function would be recomputed using the best-fit spectrum estimated in the first
step.
