Bias on Tensor-to-Scalar Ratio Inference With Estimated Covariance\n Matrices

Abstract

We investigate simulation-based bandpower covariance matrices commonly used\nin cosmological parameter inferences such as the estimation of the\ntensor-to-scalar ratio $r$. We find that upper limits on $r$ can be biased low\nby tens of percent. The underestimation of the upper limit is most severe when\nthe number of simulation realizations is similar to the number of observables.\nConvergence of the covariance-matrix estimation can require a number of\nsimulations an order of magnitude larger than the number of observables, which\ncould mean $\\mathcal{O}(10\\ 000)$ simulations. This is found to be caused by an\nadditional scatter in the posterior probability of $r$ due to Monte Carlo noise\nin the estimated bandpower covariance matrix, in particular, by spurious\nnon-zero off-diagonal elements. We show that matrix conditioning can be a\nviable mitigation strategy in the case that legitimate covariance assumptions\ncan be made.\n