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，这些数据点具有某个测量的y值，作为固定x值的函数。y值的不确定性通常表示为垂直误差条，代表每个数据点的频率主义置信区间或贝叶斯可信区间。大多数情况下，这些误差条代表68%的置信/可信水平，这导致了一种直觉：如果一个模型的预测值位于大约三分之二数据点的误差条范围内，则该模型能较好地拟合数据。不幸的是，当数据点的不确定性相关时，这种直觉以及其他直觉就不再适用。如果误差条仅显示某个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，那么我们仅从图中就无法获得足够的信息来判断所绘制的模型线是否与数据吻合。在本文中，我们将演示这个问题，并讨论如何在图中添加更多信息，以便更容易判断数据与某个模型预测在图中是否一致，并洞察模型可能存在不足的地方。这是通过明确显示不确定性第一主成分的贡献，以及展示所有数据点的条件不确定性来实现的。