忽略相关性会导致EFT预测中的模型误差误估
Neglecting correlations leads to misestimated model errors in EFT predictions
AI总结：
本文研究了EFT预测中截断误差和LECs不确定性的相互作用，揭示了相关性对理论不确定性的降低作用。
摘要：
贝叶斯分析有效场论（EFT）收敛模式能够估计由截断展开引起的不确定性。当一个已校准到数据的EFT用于预测时，这种截断不确定性以两种方式进入后验预测分布：直接来自预测量的有限阶计算，以及间接通过由校准确定的EFT低能常数（LECs）的后验概率分布。在本文中，我们关注这两种不确定性来源的相互作用。我们是在一个拟合伪数据的玩具EFT的背景下进行的，并用其进行预测。当预测量与用于拟合LECs的观测量相关时，直接的EFT截断不确定性和LECs不确定性和相关。这里这导致EFT预测中的总体理论不确定性比由截断误差引起的不确定性或仅来自LECs的不确定性要小。
英文摘要：
Bayesian analyses of the convergence pattern of Effective Field Theories (EFTs) enable estimation of the uncertainty induced by a truncated expansion. When an EFT that has been calibrated to data is used to make a prediction this truncation uncertainty enters the posterior predictive distribution twice: directly from the finite-order calculation of the predicted quantity and indirectly through the posterior probability distributions of the EFT low-energy constants (LECs) determined by the calibration. In this work, we focus on the interplay of these two sources of uncertainty. We do this in the context of a toy EFT that we fit to pseudodata and use to make predictions. Direct EFT truncation uncertainty and LEC uncertainty are correlated in predictions when the predicted quantity is correlated with the observables used to fit the LECs. Here this results in the overall theoretical uncertainty in the EFT prediction being smaller than either the uncertainty induced by the truncation error or that stemming from the LECs alone.
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