Goodness--of--fit Statistics and CMB Data Sets

Application of a Goodness--of--fit (GOF) statistic is an essential element of parameter estimation. We discuss the computation of GOF when estimating parameters from anisotropy measurements of the cosmic microwave background (CMB), and we propose two GOF statistics to be used when employing approximate band--power likelihood functions. They are based on an approximate form for the distribution of band--power estimators that requires only minimal experimental information to construct. Monte Carlo simulations of CMB experiments show that the proposed form describes the true distributions quite well. We apply these GOF statistics to current CMB anisotropy data and discuss the results.