Approximating the Likelihood Function of CMB Experiments

Abstract

We discuss the problem of constraining cosmological parameters with cosmic microwave background band--power estimates. Because these latter are variances, they do not have gaussian distribution functions and, hence, the standard $χ^2$--approach is not strictly applicable. A general purpose approximation to experimental band--power likelihood functions is proposed, which requires only limited experimental details. Comparison with the full likelihood function calculated for several experiments shows that the approximation works well.

To be published in ``The CMB and the Planck Mission'', proceedings of a workshop held in Santander, Spain, June 1998