A very common task in data visualization is to plot many data points with some measured y-value as a function of fixed x-values. Uncertainties on the y-values are typically presented as vertical error bars that represent either a Frequentist confidence interval or Bayesian credible interval for each data point. Most of the time, these error bars represent a 68\% confidence/credibility level, which leads to the intuition that a model fits the data reasonably well if its prediction lies within the error bars of roughly two thirds of the data points. Unfortunately, this and other intuitions no longer work when the uncertainties of the data points are correlated. If the error bars only show the square root of diagonal elements of some covariance matrix with non-negligible off-diagonal elements, we simply do not have enough information in the plot to judge whether a drawn model line agrees well with the data or not. In this paper we will demonstrate this problem and discuss ways to add more information to the plots to make it easier to judge the agreement between the data and some model prediction in the plot, as well as glean some insight where the model might be deficient. This is done by explicitly showing the contribution of the first principal component of the uncertainties, and by displaying the conditional uncertainties of all data points.

翻译：数据可视化中一项非常常见的任务是绘制以固定x值为函数的多个数据点及其测量得到的y值。y值上的不确定性通常以垂直误差棒表示，这些误差棒代表每个数据点的频率论置信区间或贝叶斯可信区间。大多数情况下，这些误差棒表示68%的置信/可信水平，从而产生一种直觉：如果模型的预测大约落在三分之二数据点的误差棒内，则该模型对数据拟合得相当好。不幸的是，当数据点的不确定性相关时，这种直觉及其他直觉不再成立。如果误差棒仅显示具有不可忽略的非对角线元素的某个协方差矩阵的对角元素的平方根，我们根本无法从图中获得足够信息来判断所绘制的模型线与数据是否吻合良好。在本文中，我们将演示此问题并讨论如何在图中添加更多信息，以更易于判断数据与某些模型预测之间的一致性，同时洞察模型可能存在的不足。这通过明确显示不确定性的第一主成分的贡献，以及展示所有数据点的条件不确定性来实现。