Select uncertain values by contained probability, not by mean position

Integrate each sample’s distribution inside the brush and select it only when the enclosed probability mass exceeds a chosen threshold. For example, evaluate boxes, axis intervals, or line-based brushes against the distribution area and require a high containment threshold such as 95% so broad uncertain values need a larger brush than tight certain ones.

Brushing uncertain data should respect the same uncertainty model used in the rendering. Probability-based brushing prevents a tiny brush from selecting a broad uncertain sample just because its mean happens to lie inside.

Mechanism: The brush selects distributions rather than points. A selection succeeds only when most of the distribution is actually contained, which forces the interaction to acknowledge uncertainty magnitude.

Evidence: The paper extends brushing for uncertain scatter plots and parallel coordinates by integrating each distribution within the brush and recommends a high confidence threshold, such as 95%, so uncertain values require larger brushes before they are selected (Feng et al., 2010).

• User Goal: Interactively select uncertain values without overclaiming what the brush contains.
• Task: Filter or inspect uncertain samples with box, interval, angular, or linear-function brushes.
• Data: Samples represented as statistical distributions, including normal distributions with known parameters.
• Chart Setting: Interactive scatter plots or parallel coordinates of uncertain data.
• Audience: Analysts or domain experts exploring uncertain multivariate relationships.
• Success Criterion: Selected items are mostly contained within the brush according to their distributions, not just by mean location.

Break it when: The data are treated as exact discrete samples or no distribution or PDF is available to integrate. Why: There is no probability mass to evaluate against the brush.

Sacrifice: Small quick brushes no longer select broad uncertain values. Risk: Users may think the brush is unresponsive when it correctly rejects high-uncertainty samples. Mitigation: Increase the brush size until it encloses the desired fraction of the selected distributions.

Mistake: Select by testing whether a sample mean or line center falls inside the brush. Why it fails: A small brush can capture highly uncertain distributions even when most of their probability mass lies outside.

Failure Sign: A small brush selects broad uncertain values that visibly extend far outside the brushed region. Quick Check: Inspect any selected uncertain item and confirm that most of its distribution lies inside the brush. Stronger Test: Verify that every selected item passes the same integrated-area threshold, such as 95%.

• Replace inside-outside tests on means with integration of the distribution over the brushed region.
• For line-based brushes, integrate the distribution between bounding lines instead of checking only distance to a centerline.
• Raise the selection threshold so the brush must contain most of each selected distribution.
• Enlarge the brush when you intentionally want to include broad uncertain values.