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，是绘制大量数据点，其中测得的y值作为固定x值的函数。y值的测量不确定性通常以垂直误差棒表示，代表每个数据点的频率学派置信区间或贝叶斯可信区间。多数情况下，这些误差棒代表68%的置信/可信水平，这导致了一种直观理解：若模型预测值落在约三分之二数据点的误差棒范围内，则模型与数据拟合良好。然而不幸的是，当数据点的不确定性存在相关性时，该直观判断及其他类似方法均不再适用。若误差棒仅显示某协方差矩阵对角元素的平方根，而该矩阵的非对角元素不可忽略，则我们无法从图中获取足够信息来判断绘制的模型曲线与数据是否一致。本文将以该问题为切入点，探讨如何在图中添加更多信息以更便捷地判断数据与模型预测的一致性，并从中洞察模型可能存在的缺陷。具体方法包括显式展示不确定性第一主成分的贡献，以及显示所有数据点的条件不确定性。