### Mathematics Colloquium

# Robert M. Kirby

### (Scientific Computing Institute, University of Utah, SLC)

## "Ensemble Visualization and Uncertainty Characterization Using Generalized Notions of Data Depth"

** Date: ** |
Mon, April 11, 2016 |

** Time: ** |
17:15 |

** Place: ** |
Research II Lecture Hall |

**Abstract:**
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 as well. In such situations, using ensembles is a common approach to account for the uncertainty or, in a broader sense, explore 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 (from scalar or vector fields). This class of visualization techniques is based on the generalization of conventional univariate boxplots. Generalizations of boxplot provide an intuitive yet rigorous approach to studying variability while preserving the main features shared among the members. They also aid 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 makes it an advantageous approach to study uncertainty in various applications ranging from image analysis to fluid simulation to weather and climate modeling.

*The colloquium is preceded by tea from 16:45 in the Resnikoff Mathematics Common Room, Research I, 127.*