Ensemble Visualization and Uncertainty Characterization Using Generalized Notions of Data Depth

Mahsa Mirzargar

When computational methods or predictive simulations are used to model complex phenomena such as dynamics of physical systems, researchers, analysts and decision makers are not only interested in understanding the data but also interested in understanding the uncertainty present in the data. In such situations, using ensembles is a common approach to accounting for the uncertainty or, in a broader sense, exploring the possible outcomes of a model. Visualization, as an integral component of data analysis task, can significantly facilitate the communication of the characteristics of an ensemble including uncertainty information. Designing visualization schemes suitable for exploration of ensembles is specifically challenging if the quantities of interest are derived feature-sets such as isocontours or streamlines rather than fields of data.

In this talk, I will introduce novel ensemble visualization paradigms that use a class of nonparametric statistical analysis techniques called data depth to derive robust statistical summaries from an ensemble of feature-sets. This class of visualization techniques is based on the generalization of conventional univariate boxplots. Generalizing boxplots provides an intuitive yet rigorous approach to studying variability while preserving the main features shared among the members. It also aids in highlighting descriptive information such as the most representative ensemble member (median) and potential outlying members. The nonparametric nature and robustness of data depth analysis and boxplot visualization make such ensemble visualization schemes an advantageous approach to studying uncertainty in various applications ranging from image analysis to fluid simulation to weather and climate modeling.