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

TL;DR

This paper reveals that using estimated covariance matrices from simulations in cosmological parameter inference can bias the tensor-to-scalar ratio estimates, especially with limited simulations, and discusses mitigation strategies.

Contribution

It identifies the bias introduced by simulation-based covariance matrices in tensor-to-scalar ratio inference and proposes matrix conditioning as a mitigation approach.

Findings

Upper limits on r can be biased low by tens of percent.

Convergence of covariance estimation may require an order of magnitude more simulations.

Spurious off-diagonal elements cause additional scatter in posterior estimates.

Abstract

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