The session on statistical uncertainty will explore the use of statistics for quantification and visualization of uncertainty. The session will begin by exploring the use of statistics in understanding complex problems and describe the look of typical datasets created in this way. From there, I will discuss challenges to the display of these complex data sets, and statistical measures specific to expressing uncertainty within visualization. The remainder of the session will focus on visualization methods, including a recounting of historical methods from the field of graphical data analysis including the boxplot, as well as an overview of methods from scientific and information visualization. Examples of current state-of-the art methods will be presented and a final wrap-up will discuss pending challenges in need of further exploration.

• Introduction
• Define statistical uncertainty
• Methods for quantification
• Data
• Ensembles (multi-simulation runs)
• PDFs (stochastic solves)
• Uncertainty measures for visualization
• Moments
• Difference measures
• Visualization methods
• 2D graphical techniques (historical methods from exploratory data analysis)
• 2D, 3D sci vis methods
• Future directions/unanswered questions

The core contributions of this session are a) explain the use of statistics to quantify uncertainty b) explore statistical measures used for visualization c) tour historic as well as state-of-the art statistical uncertainty visualization techniques and d) gain an idea of what the upcoming challenges in this work are.

• K. Potter, J.M. Kniss, R. Riesenfeld, C.R. Johnson. “Visualizing Summary Statistics and Uncertainty,” In Computer Graphics Forum (Proceedings of Eurovis 2010), Vol. 29, No. 3, pp. 823--831. 2010.
• K. Potter, J. Krueger, C.R. Johnson. “Towards the Visualization of Multi-Dimensional Stochastic Distribution Data,” In Proceedings of The International Conference on Computer Graphics and Visualization (IADIS) 2008, pp. 191--196. 2008.
• K. Potter, R.M. Kirby, D. Xiu, C.R. Johnson. “Interactive Visualization of Probability and Cumulative Density Functions. In The International Journal of Uncertainty Quantification (to appear), 2012.

• C.R. Johnson. “Top Scientific Visualization Research Problems,” In IEEE Computer Graphics and Applications: Visualization Viewpoints, Vol. 24, No. 4, pp. 13--17. July/August, 2004.
• C.R. Johnson, A.R. Sanderson. “A Next Step: Visualizing Errors and Uncertainty,” In IEEE Computer Graphics and Applications, Vol. 23, No. 5, Edited by Theresa-Marie Rhyne, pp. 6--10. September/October, 2003
• Udeepta D. Bordoloi and David L. Kao and Han-Wei Shen."Visualization techniques for spatial probability density function data". In Data Science Journal, vol. 3, pp. 153--162, 2004.
• David Kao, Alison Luo and Jennifer L. Dungan and Alex Pang. "Visualizing Spatially Varying Distribution Data". In Proceedings of the Sixth Int’l Conference on Information Visualization, pp. 219--225, 2002.
• Chris Olston and Jock D. Mackinlay."Visualizing Data with Bounded Uncertainty". In Proceedings of the IEEE Symposium on Information Visualization (InfoVis'02), pp. 37--40, 2002.
• Kristin Potter. Methods for Presenting Statistical Information: The Box Plot. In Hans Hagen, Andreas Kerren, and Peter Dannenmann (Eds.), Visualization of Large and Unstructured Data Sets, GI-Edition Lecture Notes in Informatics (LNI), Vol. S-4, pp. 97-106, 2006.
• Jibonananda Sanyal and Song Zhang and Jamie Dyer and Andrew Mercer and Philip Amburn and Robert J. Moorhead. "Noodles: A Tool for Visualization of Numerical Weather Model Ensemble Uncertainty". In IEEE Transactions on Visualization and Computer Graphics, vol. 16, no. 6, pp. 1421 - 1430, 2010.
• Alexander Streit and Binh Pham and Ross Brown. "A Spreadsheet Approach to Facilitate Visualization of Uncertainty in Information". In IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 1, pp. 61--72, 2008.
• Barry N. Taylor and Chris E. Kuyatt."Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results". Technical Report, NIST Technical Note 1297, 1994.

Scientific Computing and Imaging Institute, University of Utah

Kristin Potter is currently a Research Scientist at the SCI Institute. In 2010 she received her Ph.D. from the University of Utah and began life as a computer scientist at the University of Oregon, where she earned her B.S. in computer science and fine arts. Her current research focuses on the integration of uncertainty into visualization. This work draws from the fields of scientific and information visualization and uncertainty quantification and is motivated by the need to increase the utility of visualization as a decision making tool. By visually describing the uncertainties present in a display, a scientist will be better informed on the quality of the data and thus be capable of making improved and more confident decisions. The greatest challenge to this work is in understanding the sources and quantifications of the uncertainty and in designing effective visual metaphors.