Uncertainty Visualization: How to Make it Interpretable, Integrable, and Accessible?bookmark_border

Uncertainty visualization has been shown to be pivotal for conveying the reliability of features extracted from scalar fields. Features represented by individual isocontours and mean isocontours lack an indication of spatial uncertainty, whereas spaghetti isocontour plots can become cluttered and difficult to interpret. Existing methods relying on specific distribution assumptions, such as Gaussian and nonparametric bootstrap, provide compact, clutter-free spatial confidence bounds but may underestimate uncertainty for ensembles with a limited number of samples. We introduce a robust, distribution-agnostic Hoeffding confidence band as a novel complementary (and not competitive) technique to mitigate potentially misleading uncertainty bounds that may arise from distribution-based assumptions. The approach constructs vertex-wise confidence bounds using Hoeffding's inequality and propagates them to generate isocontour confidence bands. Results on synthetic and real ensemble datasets show that the Hoeffding confidence bands are loose but accurately capture underlying true values that may be missed by the Gaussian and bootstrap alternatives, while remaining computationally efficient.

Women returning to grassroots football after motherhood navigate uncertainty not only about physical readiness, but also confidence, time, childcare, belonging, and whether participation can be sus- tained as circumstances change. We investigate how visualisation can represent this form of lived uncertainty without reducing per- sonal experiences to probabilistic estimates or prescribing a norma- tive pathway. Guided by the Empathy-Driven Visualisation Frame- work (EDVF) and Five Design Sheets (FDS), we followed an itera- tive, human-centred design process grounded in direct engagement with a grassroots women’s football community. This process in- formed the development of Field Guide, a narrative visualisation representing return through revisitable participation states, multi- ple trajectories, shared experiences, and thematic exploration. We conducted an online participant study with 39 mothers involved in grassroots football, and identified five interacting dimensions of lived uncertainty. Preliminary evaluation of Field Guide indicated perceived value in encountering other mothers’ experiences, partic- ularly through validation, normalisation, and reflection. Rather than predicting readiness or defining a successful return, Field Guide explores how narrative visualisation can make multiple possible fu- tures visible while preserving the personal and socially situated na- ture of uncertainty. We contribute a characterisation of lived uncer- tainty in return-to-play, an account of its representation through an iterative narrative visualisation design, and design considerations for making lived uncertainty more interpretable, integrable, and ac- cessible within sensitive, human-centred contexts.

Woven artifacts communicate through more than printed or stitched marks: dye saturation, yarn integrity, weave density, thread path, interlacement, and surface relief all shape what can be seen. This paper asks whether controlled changes to those material properties can communicate uncertainty as part of the artifact itself. We develop a vocabulary comprising faded dye, thinning weave, fraying, pulled threads, and puckering. Their consequences for reading fall into four categories: loss of visible support, dispersion of detail, displacement of position, and production of spurious structure. These categories correspond to suppressive, diffusive, displacive, and generative effects, respectively. Unravelling junctions are treated separately as a possible means of expressing uncertainty about relations. The analysis highlights both potential mappings and textile-specific hazards, including associations with age, damage, care, neglect, repair, and decay. The contribution is a conceptual framework and evaluation agenda but the proposed operations have not yet been established as perceptually calibrated uncertainty encodings.

Mapper graphs provide compact topological summaries of high-dimensional data, but small changes in cover parameters can substantially alter their topology, making it difficult to distinguish persistent structures from those that arise only under particular parameter configurations. Despite growing interest in uncertainty visualization, methods for representing uncertainty in Mapper graphs remain largely unexplored. We present LoCoMapper, a framework that takes a first step toward uncertainty-aware visualization of Mapper graphs by characterizing their local structural sensitivity to perturbations of the cover parameters. Given a reference Mapper graph, LoCoMapper aligns local regions of the reference graph with corresponding regions in an ensemble of perturbed graphs and summarizes their variation using two node-level measures: local structural consistency, which quantifies the preservation of local topology across reliable alignments, and ensemble support, which captures the amount of reliable evidence supporting that estimate. Jointly visualizing these measures on the reference graph enables users to distinguish robust, sensitive, and weakly supported regions. We demonstrate the effectiveness of LoCoMapper on a controlled two-dimensional dataset, a synthetic three-dimensional ant dataset, and word embeddings from a fine-tuned BERT model.

Uncertainty visualization is an important tool for helping people make decisions based on estimates, predictions, and other sources of uncertain information. Designing and evaluating the extent to which different visualizations support optimal decision-making is an ongoing effort. In this short paper, we review evidence that purposeful practice with a visualization can substantially improve task performance, and that the rank ordering of task performance using visualizations can change before and after practice. Providing opportunities for practice might not always be practical in every application, but during evaluation it can be helpful to characterize how performance changes with practice to provide a fuller understanding of performance attributable to the visualization used.

Prediction market platforms present contracts about future events through visualizations that show probabilities, prices, trends, odds, and payout information. Although these visualizations often appear precise, they do not always show uncertainty directly. As a result, users infer uncertainty from market movement, visualization cues, and contextual information. In this paper, we examine how users interpret prediction market visualizations through a qualitative analysis of posts and comments from the Reddit community r/Kalshi. From an initial corpus of approximately 12,000 posts and 96,000 comments, we identified 360 posts containing prediction market visualizations and conducted a thematic analysis of annotated posts and related discussions. Our findings show that users infer uncertainty through several forms of interpretation: they interpret chart values, struggle with probability information displayed, bring in external knowledge, question credibility and liquidity, critique visualization design, and connect visualized information to betting decisions.

Uncertainty visualizations often require viewers to interpret additional marks, glyphs, bands, or statistical conventions layered onto a primary display. We explore a complementary approach: rendering uncertainty as an optical condition of seeing. In this framing, data are viewed through an imperfect medium whose apparent physical properties are controlled by uncertainty. We introduce a design vocabulary of optical operations for uncertainty visualization, including blur, frost, absorption, roughness, thickness, microfacet scattering, refraction, and caustics. We organize these operations by how they affect visual information: suppressive operations reduce visibility, diffusive operations reduce recoverability, displacive operations alter apparent position, and generative operations create new apparent structure. This distinction suggests a mapping between degradation and value uncertainty, and between displacement and positional uncertainty, while identifying caustics and other structure-generating effects as high-risk sources of visual confounds.

Survey results are routinely summarized with scalar measures of agreement to compare questionnaire items, yet those summaries are hard to interpret on bounded rating scales. Most uncertainty visualizations communicate uncertainty by representing multiple possible values, estimates, or outcomes. We consider a complementary source: the responses and the computed agreement score are fixed, but the meaning of that score depends on where it sits on the scale. Because responses have less room to spread near the endpoints of a five-point Likert item, agreement there is mechanically constrained, so the same score can arise from very different distributions and can imply different consensus at different rating levels. We call this ambiguity agreement uncertainty; collecting more responses does not resolve it, since the score must instead be read against the feasible agreement space at its rating level. We introduce residual consensus, a calibration that expresses agreement relative to what the scale allows, informative only where that space has enough resolution and therefore read alongside the response distribution itself. Drawing on ideas from possibility-framing and meta-uncertainty in uncertainty visualization, we contribute a coordinated view that shows calibrated agreement, its positional informativeness, and the distribution together, demonstrated on real-world survey datasets to support more meaningful comparisons across bounded scales.

Affective visualization can influence how users perceive, interpret, and engage with data by embedding and conveying emotion through visual design. While sound is widely used in media to evoke emotions, little is known about how sonification can support affective visualization. In this work, we investigate how sonification can communicate emotion in uncertainty visualizations through a co-design study. Participants created two sonifications to accompany a visualization: one conveying the affective component of uncertainty and one conveying neutrality. Our findings show that uncertainty was commonly associated with wavy auditory qualities related to an ominous sentiment. On the other hand, neutrality was associated with clear and relaxing auditory qualities. These results provide insights for the design of visualizations that integrate sonification to communicate the affective component of uncertainty.

We present an uncertainty-aware Jacobi set computation method. In general, Jacobi sets are topological descriptors that capture the gradient alignments of two scalar fields, as, e.g., used for multi-field visualization. We adopt and reformulate an existing computational approach that relies on an edge-based identification of Jacobi set edges on a given triangulation. Our extension to uncertainty visualization builds upon a versatile, spatially coherent uncertainty model for pairs of scalar fields based on multivariate normal distributions. We propagate the uncertainty analytically, thereby lifting the original Jacobi set computation to uncertain inputs. Furthermore, we present an overlay of visual mappings specifically designed to show the Jacobi sets along with different facets of uncertainty information. Both the uncertainty model and uncertainty-aware method are validated against a Monte Carlo approach on an analytic dataset and applied to two use cases from fluid dynamics and weather ensembles.

Widely used non-linear dimensionality reduction (NLDR) methods such as UMAP and t-SNE are stochastic---repeated runs on the same data can produce different low-dimensional projections. In this paper, we explore two problems related to projection variability: on some datasets clusters, structure, and outliers may change run-to-run, and on others projections can be extremely stable when overfitting noise. To address the first problem, we propose visualizing the median of multiple NLDR outputs rather than relying on individual projections. To address the second, we perturb input data before creating consensus embeddings. We find that taking the median of multiple projections performs comparably to individual runs on multiple quality metrics, while increasing perturbation emphasizes global over local structure. We show through a set of exploratory visualizations that even relatively simple ensemble presentations can be used to better communicate the reliability of projection patterns.

Artificial intelligence systems often disclose uncertainty, yet they rarely make clear what response that uncertainty should trigger. Most uncertainty visualizations encode uncertainty in model outputs, leaving users to discern the most appropriate course of action. A second region of the design space--uncertainty in the decision process itself, including how multiple uncertainty conditions compose into an oversight response-- remains comparatively underexplored. We address this gap with two coupled contributions. First, we introduce an uncertainty-to-action binding framework that composes multiple uncertainty conditions into a single oversight response under a precedence policy with a contextual safety modifier. That response concerns whether and how an AI-supported decision may proceed, not the substantive domain decision itself. Second, we present ActionCue, a process-transparency visualization that renders that composition explicit. We demonstrate the approach through a three-way comparison with confidence-only and data-level uncertainty displays, using worked cases from healthcare, credit assessment, and disaster forecasting. Together, the framework specifies how uncertainty conditions are resolved into an oversight response, and the visualization makes that resolution inspectable rather than implicit.