Matching Bayesian and frequentist coverage probabilities when using an approximate data covariance matrix

ABSTRACT Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important maximum a posteriori probability values, indicate concordance or discordance between models with measurements from other data. Intermediate statistics (e.g. power spectrum) usually measured made fitting to these rather than raw data, assuming that likelihood for has multivariate Gaussian form. covariance matrix used calculate is estimated simulations, such it itself random variable. This standard problem in Bayesian statistics, which requires prior be true matrix, influencing joint posterior distribution. As an alternative commonly independence Jeffreys prior, we introduce leads approximately frequentist matching coverage. achieved distribution values around repeated trials, under certain assumptions. Using this derived analysis can interpreted confidence intervals, containing truth proportion time trials. Linking approaches have previously appeared astronomical literature, offers consistent conservative approach quoted problems where estimate.