5 Conclusion
The three papers presented in this thesis share a common theme of communicating uncertainty in a way that it can be seen. These papers present a cohesive vision for the future of uncertainty visualisation, one that is defined within the infrastructure set by statistical graphics. We established the foundations of this vision by approaching the uncertainty visualisation problem from three separate angles: the philosophical goals of the field, the practical limitations of the mathematical objects we are working with, and the human perception of uncertainty in visualisation.
5.1 Contributions
This thesis makes several important contributions to the uncertainty visualisation literature.
First, Chapter 2 offers a philosophical foundation for the future of uncertainty visualisation that resolves the ongoing conflicts that currently plague the field. By connecting our evaluation of uncertainty visualisation back to its primary purpose, we are able to map out what it actually means to “see” uncertainty in a visualisation. Using this context, we illustrate that much of the conflict in the literature comes from a mismatch between the stated goals and evaluation methods utilised by the field. These insights allow us to present a cohesive vision for the future of uncertainty visualisation, built upon the goal of visualising uncertainty as “noise”.
Second, Chapter 3 presents two key contributions: a mathematical framework for uncertainty visualisation, and the introduction of the ggdibbler R package. The mathematical framework presents the argument that the grammar of graphics is a continuous function, and therefore, statistical graphics should adhere to the continuous mapping theorem. The key insights of this formalisation are translated into the flexible uncertainty visualisation software, ggdibbler, the second contribution from this chapter. The ggdibbler software allows us to substitute any vector of values with a vector of random variables, and make an uncertain version of any graphic that can be made in ggplot2. This software received the 2026 John Chambers Award for Statistical Software from the ASA Sections on Statistical Computing and Statistical Graphics, it has 21 stars on GitHub, and has been downloaded over 1800 times on CRAN since it was uploaded in July 2025. This indicates the value the statistics community has placed on flexible uncertainty visualisation software that can be used for EDA.
Finally, Chapter 4 uses the mathematical formalisation of Chapter 3 in a perceptual evaluation of choropleth maps to confirm the hypotheses discussed in Chapter 2. Evaluating uncertainty as noise required the development of a new experimental methodology that is able to measure the effect of a latent variable (noise) on an observable variable (signal). The results of this paper show that visualising a distribution as a set of samples is not only the most flexible approach (as established by Chapter 3), but it is also the approach that most accurately conveys the results of standard statistical tests.
5.2 Future work
There are several avenues one could take to improve upon this work; we will list the most important ones here.
5.2.1 ggdibbler software
The full list of improvements and fixes that should be made to ggdibbler can be seen on the package’s GitHub issues. In this section, we will touch on some of the high-level improvements that could be made to the software.
One of the core assumptions of the software is that it assumes each individual cell of our table is a distribution, and these distributions are completely independent. This assumption can be quite strict, and the most natural improvement to the software would be to allow users to pass joint distributions to allow for dependency between cells in the random matrix. The theoretical framework already allows for this, as does the underlying distributional package; the only limitation currently imposed is by the ggdibbler software. However, implementing this change is not straightforward, as it would require us to reach inside the joint distribution to map variables, and could possibly require bespoke syntax to get the extension working.
Another improvement to the software is the flexibility to allow any object type. Similarly to the joint distributions, this is already allowed by the theoretical foundations as well as distributional. Practically, this would require us to set up a nested distribution scale for all scale types. That is, currently the software replaces scale_x_continuous with scale_x_continuous_distribution, which works for continuous data, but ggplot2 also has scales such as scale_x_datetime, which does not have a scale_x_datetime_distribution counterpart. While it would be straightforward to implement this with the existing ggplot2 supported scales, much of the benefit of ggplot2 comes from its network of extensions that allow for many different object types. Implementing ggdibbler with ggplot2 extensions is an issue that goes beyond scales, and similar limitations exist with stats and positions. Implementing some kind of “function factory” or wrapper solution might give us the flexibility needed to allow ggdibbler to work with all input types, these developments are still a work in progress.
5.2.2 Latent variable testing for all aesthetics
While a variation of the Ishihara colour blind tests allowed us to measure uncertainty as a latent variable, this approach is only viable when we have mapped our random variable to colour. The theoretical framework developed for uncertainty visualisation should allow us to map uncertainty to any aesthetic in any combination. Designing similar experiments for the most commonly used aesthetics (including position, shape, length, etc.) would serve as a value baseline for the evaluation of uncertainty in statistical graphics.
5.2.3 A fundamental theory of visualisation
Many elements of this thesis point towards a more fundamental theory of visualisation that can be tied to the grammar of graphics. This alternative connection would allow us to better formalise our graphics as mathematical objects, which, as illustrated by Chapter 3 and Chapter 4, would facilitate more flexible plot design and more informative perceptual experiments. This fundamental theory of visualisation would allow us to treat visualisations as statistics with desirable statistical properties, such as statistical sufficiency, bias, and variance. This line of thinking is similar to the argument made by Wickham and Hofmann (2011) in their discussion of product plots. The authors draw a link between statistical graphics and their underlying distributions using the fact that both geometry and probability are born from measure theory. Strengthening this connection is likely a good avenue for future research.