A quantitative analysis of any environment older than the instrumental record relies on proxies. Uncertainties associated with proxy reconstructions are often underestimated, which can lead to artificial conflict between different proxies, and between data and models. In this paper, using ordinary least squares linear regression as a common example, we describe a simple, robust and generalizable method for quantifying uncertainty in proxy reconstructions. We highlight the primary controls on the magnitude of uncertainty, and compare this simple estimate to equivalent estimates from Bayesian, nonparametric and fiducial statistical frameworks. We discuss when it may be possible to reduce uncertainties, and conclude that the unexplained variance in the calibration must always feature in the uncertainty in the reconstruction. This directs future research toward explaining as much of the variance in the calibration data as possible. We also advocate for a “data-forward” approach, that clearly decouples the presentation of proxy data from plausible environmental inferences.

中文翻译：

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古气候代理重建的统计不确定性

任何比仪器记录更早的环境的定量分析都依赖于代理。与代理重建相关的不确定性通常被低估，这可能导致不同代理之间以及数据和模型之间的人为冲突。在本文中，我们以普通最小二乘线性回归为例，描述了一种简单、稳健且可推广的方法，用于量化代理重建中的不确定性。我们强调了对不确定性大小的主要控制，并将这个简单的估计与贝叶斯、非参数和基准统计框架的等效估计进行了比较。我们讨论了何时可以减少不确定性，并得出结论，校准中无法解释的方差必须始终体现在重建的不确定性中。这将引导未来的研究尽可能多地解释校准数据中的差异。我们还提倡一种“数据转发”方法，该方法清楚地将代理数据的呈现与合理的环境推断脱钩。