Likelihood, Fisher information, and systematics of cosmic microwave
  background experiments
  Every experiment is affected by systematic effects that hamper the data
analysis and have the potential to ultimately degrade its performance. In the
case of probes of the cosmic microwave background (CMB) radiation, a minimal
set of issues to consider includes asymmetric beam functions, correlated noise,
and incomplete sky coverage. Presuming a simplified scanning strategy that
allows for an exact analytical treatment of the problem, we study the impact of
systematic effects on the likelihood function of the CMB power spectrum. We use
the Fisher matrix, a measure of the information content of a data set, for a
quantitative comparison of different experimental configurations. In addition,
for various power spectrum coefficients, we explore the functional form of the
likelihood directly, and obtain the following results: The likelihood function
can deviate systematically from a Gaussian distribution up to the highest
multipole values considered in our analysis. Treated exactly, realistic levels
of asymmetric beam functions and correlated noise do not by themselves decrease
the information yield of CMB experiments nor do they induce noticeable coupling
between multipoles. Masking large fractions of the sky, on the other hand,
results in a considerably more complex correlation structure of the likelihood
function. Combining adjacent power spectrum coefficients into bins can
partially mitigate these problems.
