Visualizing Uncertainty in Dynamic Variables

How to visualize an uncertainty in a time-dependent variable according to the principles of uncertainty visualization?

We have a trajectory is a time-space, but we don’t know exactly where it is. One of the simplest way way to visualize such data is a ‘spaghetti-plot’:

Here each line in Figure is one possible trajectory. This Figure is already very efficient, but it may be influenced by the choice of visualized possibilities. For example:

vis0 - копияis there actually no chance the trajectory would pass through the area marked with ???, or it is just a coincidence that none of randomly selected visualized trajectories did so?

Visualizing a confidence intervals is a completely different approach. Instead of individuals possibilities, summary statistics are presented.


Here light blue colour marks the 99% confidence area (i.e. area where 99% of the trajectories go), while dark blue represent the 50% interval.

The confidence figure solves the problem of a ‘spaghetti-plot’ (The answer to the previous question is NO, it was just a coincidence). But it violates a few principles of uncertainty visualization: it may overemphasize the median estimates, and it stresses uncertain values over certain ones.

Simple solution (which could be not so trivial in the actual implementation): instead of fixed shades, dilute a colour concentration with the growth of the represented area:



This Figure consists of five ‘ribbons’, representing 1-20, 20-40, 60-80 and 80-99 percentile intervals of the trajectories. Colour of the ‘ribbon’ depend on its width. This Figures naturally points out the most certain (i.e. interesting) estimates.

Both the original and updated confidence figures had a problem. Summary statistics hide a lot of information. They don’t show is the trajectories are smooth or noisy, or if they are correlated. The solution would be to combine  a ‘confidence plot’ with a ‘spaghetti plot’ and to put a few possible trajectories under the confidence intervals:




Visualizing Uncertainty in Dynamic Variables

One thought on “Visualizing Uncertainty in Dynamic Variables

  1. Peter P. says:

    I love your examples and your reasoning behind each option! One alternative that I find myself using lately–and which I don’t think is pictured here–is a spaghetti plot consisting of the *entire* posterior distribution (many thousands of lines) rather than a random subsample. I draw each line at very high transparency (e.g., alpha=.01), and the result usually ends up looking a like a confidence interval, but you get the natural subjective impression of depth proportionate to the density of the posterior. I like seeing this full “cloud” of estimates, and this way, you get to see the occasional spaghetti strand that extends beyond the 99th percentile, as a reminder of the uncertainty in the overall estimate.


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