论文标题
与估计协方差矩阵的张量与量表比的偏差
Bias on Tensor-to-Scalar Ratio Inference With Estimated Covariance Matrices
论文作者
论文摘要
我们研究了基于仿真的带能力协方差矩阵，通常用于宇宙参数推断，例如张张量比比率$ r $ $ $ r $。我们发现，$ r $上的上限可能会偏向数百分之百分百。当模拟实现的数量与可观察到的数量相似时，上限的低估最为严重。协方差 - 矩阵估计的收敛性可能需要许多模拟一个比观察值数量大的数量级，这可能意味着$ \ MATHCAL {O}（10 \ 000）$模拟。发现这是由于$ r $ $ r $的额外散布引起的，这是由于估计的带能量协方差矩阵中的蒙特卡洛噪声，特别是由虚假的非零异构元件。我们表明，在合法的协方差假设的情况下，矩阵条件可能是一种可行的缓解策略。
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.
