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Large-scale spatial density datasets, such as galaxy distributions, crime incidents, disease outbreaks, and nighttime light intensity, often exhibit complex geometric and topological structure. A density ridge captures the backbone of high-density regions, where data concentrate and the density attains local maxima in directions orthogonal to the structure. Detecting and constructing such ridges is fundamental to applications in urban analytics, road networks, and cosmology. For example, density ridges of crime incidents reveal hotspots that inform patrol allocation, while ridges in galaxy distributions characterize the filamentary structure of the cosmic web. In this paper, we extract uncertainty-aware density ridges from kernel density estimates (KDEs) using Morse complexes. Rooted in Morse theory, Morse complexes provide a gradient-based topological abstraction of density fields. Their one-dimensional skeletons, referred to as Morse skeletons, connect saddle points to local maxima and naturally serve as representations of density ridges. However, these skeletons are sensitive to small perturbations in the data; certain regions exhibit pronounced instability, limiting their reliability as visualization and analysis primitives. To address this limitation, we quantify uncertainty in Morse skeletons and identify structurally stable regions that support the detection and characterization of filamentary structures. Our approach aggregates Morse complexes across an ensemble of perturbed datasets to produce an uncertainty heatmap. In addition, we introduce an optimized coreset construction for KDE that is compact while preserving the Morse complex structure of the original data. Through experiments on diverse applications, including patrol planning, traffic routing, and cosmic web reconstruction, we show that our uncertainty heatmaps characterize structural stability and enhance robustness, while our coresets enable efficient computation without compromising topological fidelity.

Forecasting involves multiple forms of uncertainty, including both uncertainties that can be quantified directly (quantitative uncertainty) and those that must be expressed through experts’ subjective judgments about the forecast and its context (qualitative confidence). Past work has established that conveying both quantitative uncertainty and qualitative confidence in forecasts can alter readers’ decision making, but little research investigates the impact of how these forms of uncertainty are presented. In this work, we present three preregistered human-subjects studies (total n = 923) on how different methods of visualizing qualitative uncertainty alongside line charts' confidence intervals affects non-experts' decision making. In particular, we investigate representing qualitative uncertainty separately via text and icons, and integrated into quantitative confidence intervals via color, transparency, and a blurred stroke design. In Experiment 1, we confirm that showing qualitative confidence alongside statistical variability can change patterns of decision making, replicating findings from previous work in the new context of time-series line charts. In Experiments 2 and 3, we find several non-textual encoding techniques that produce similar effects in participants' incorporation of qualitative confidence into their judgments. Our findings suggest actionable guidelines for visualization designers who seek to represent multiple forms of uncertainty for a single line chart forecast. A free copy of this paper and all supplemental materials are available at https://osf.io/7ya2c/overview.

We present a general approach to visualizing uncertainty in static 2-D statistical graphics. If we treat a visualization as a function of its underlying quantities, uncertainty in those quantities induces a distribution over images. We show how to aggregate these images into a single visualization that represents the uncertainty. The approach can be viewed as a generalization of sample-based approaches that use overlay. Notably, standard representations, such as confidence intervals and bands, emerge with their usual coverage guarantees without being explicitly quantified or visualized. As a proof of concept, we implement our approach in the IID setting using resampling, provided as an open-source Python library. Because the approach operates directly on images, the user needs only to supply the data and the code for visualizing the quantities of interest without uncertainty. Through several examples, we show how both familiar and novel forms of uncertainty visualization can be created. The implementation is not only a practical validation of the underlying theory but also an immediately usable tool that can complement existing uncertainty-visualization libraries.

The influence of linguistic bias in online news articles is a growing concern, particularly in the context of shaping public opinion and rising political polarization. While there is a growing body of literature on indicators for misinformation, none have been sufficiently tested to counteract the influence of media bias. Hence, we design six indicators (Bias Bar, Bias Gauge, Bias Highlights, Political Scale, Sentiment Scale, and Trust Score) and test their impact on linguistic bias detection and perception in a two-phased experiment (n = 214). First, we expose participants to short, social-media-like statements along with one indicator and query bias perception. Second, we evaluate bias detection by removing the indicator and asking participants to mark biased words. In addition, we examine how trust, sharing discernment, and sentiment relate to bias perception and detection. Our results show that highlighting biased phrases and showing total bias with contextual information in a gauge significantly improve bias detection skills. However, the strongest predictor for reduced bias detection was political congruency between the statement and the participant. We conclude with design recommendations for linguistic media bias indicators in online news environments.

Forecasts often diverge because different models make varying assumptions to account for underlying uncertainty. Readers who consume forecasts may wish to survey the shape and spread of these multiple forecasts to get a full account of the different predictions. One approach to visualizing multiple forecasts is through Confidence Interval (CI) plots. However, while the summative CI plots can communicate uncertainty of an ensemble, they obscure attributes of individual forecasts that can lead to inaccurate perceptions of the distribution of these forecasts (e.g., implying a normal distribution when non-existent). To address this challenge, we investigate the use of multiple forecast visualization (MFV) in communicating nuanced forecast distributions through two preregistered experiments using climate forecast data. In Experiment 1 (480 participants), we compared how well MFV and CI plots can represent the distribution of multiple forecasts. We found that, compared to CI plots, MFV improved participants' ability to identify the underlying distribution of forecasts and reduced the likelihood of assuming normality. Building on Experiment 1, we examined in Experiment 2 (900 participants) whether a downsampled MFV showing 9 forecasts might be able to communicate additional forecast properties using linewidth and opacity without negatively impacting distribution perception. We found that visually weighting forecasts by linewidth or opacity preserves readers' perception of the underlying distribution. We discuss how these findings suggest the use of downsampled and weighted MFV to cut through forecast clutter by aligning perceived distribution with the underlying forecast distribution, while opening up design opportunities to use weighting to communicate additional forecast attributes.

We present a new visualization method for contour ensembles through probabilistic modeling. We aim to improve the coherence between different visual representations, such as contour boxplots and density plots for a 2D scalar field ensemble. We model each ensemble member with a probabilistic representation in the latent space, i.e., a lower-dimensional representation of spatial data features, of a variational autoencoder (VAE). Thereafter, efficient data depth computation and uncertainty-aware clustering are supported based on a matrix of pair-wise similarity measurements of members. We estimate the underlying probability distribution by leveraging the power of VAE to create density plots that align more coherently with member distributions than existing methods. The effectiveness of our method is evaluated through numerical comparisons with existing techniques, and visualization examples of synthetic and real-world ensemble datasets.

Uncertainty visualisation is important for data transparency, especially for map visualisations where data is often aggregated. Despite the importance of this area, studies evaluating uncertainty visualisation lack consensus and produce conflicting results. This work introduces a new evaluation approach for uncertainty visualisation that attempts to assess uncertainty as noise, rather than signal. We evaluate five methods of visualising uncertainty: standard choropleth maps, value/variance bivariate maps, value-suppressing uncertainty palettes, overlaid sampling, and pixelated sampling maps. Built on principles of implicit testing, we put an 'uncertainty visualisation' spin on the classic Ishihara colourblind test to create a novel test that is able to evaluate uncertainty as noise. We compare signal visibility to conventional hypothesis tests at various levels of group separation. By building our experimental design on top of established graphics theory, we isolate the plot components that facilitate successful signal suppression and establish foundational theory for the perception of uncertainty visualisation.