用近似协方差矩阵和其他未识别偏差进行去偏推断
Debiasing inference with approximate covariance matrices and other unidentified biases
摘要：
当后验曲线在参数空间的非预期区域达到峰值时，要么是发现了新的物理学，要么是尚未发现偏差。区分这两种情况是极其重要的。因此，我们提出了一种方法来指示和减轻未识别的偏差：我们的方法在模拟和真实数据上运行任何可能存在未知偏差的管道。它计算后验的覆盖概率，衡量后验体积是否是概率的忠实表示。如果发现有必要，则对后部进行矫正。这是一个符合客观贝叶斯推断的非参数去偏过程。我们使用这种方法来消除近似协方差矩阵和红移不确定性的偏差。我们演示了为什么近似协方差矩阵偏置的物理约束，以及如何可以减轻这种偏见。我们表明，对于一个类似于欧几里得的调查，如果存在传统的可能性，那么25个端到端的模拟足以保证品质因数最大恶化22%，或者225个模拟恶化10%。因此，即使是对欧几里得数据的悲观分析，与KiDS和DES设定的最新技术水平（2018年）相比，暗能量参数的精度仍将提高25倍。我们提供了我们方法的公共代码。
英文摘要：
When a posterior peaks in unexpected regions of parameter space, new physics has either been discovered, or a bias has not been identified yet. To tell these two cases apart is of paramount importance. We therefore present a method to indicate and mitigate unrecognized biases: Our method runs any pipeline with possibly unknown biases on both simulations and real data. It computes the coverage probability of posteriors, which measures whether posterior volume is a faithful representation of probability or not. If found to be necessary, the posterior is then corrected. This is a non-parametric debiasing procedure which complies with objective Bayesian inference. We use the method to debias inference with approximate covariance matrices and redshift uncertainties. We demonstrate why approximate covariance matrices bias physical constraints, and how this bias can be mitigated. We show that for a Euclid-like survey, if a traditional likelihood exists, then 25 end-to-end simulations suffice to guarantee that the figure of merit deteriorates maximally by 22 percent, or by 10 percent for 225 simulations. Thus, even a pessimistic analysis of Euclid-like data will still constitute an 25-fold increase in precision on the dark energy parameters in comparison to the state of the art (2018) set by KiDS and DES. We provide a public code of our method.
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