Dr. Balch's doctoral work was funded by NASA Langley through the National Institute of Aerospace (NIA) in Hampton, VA. The goal of this project was to quantify uncertainty in the inputs to a Mars atmosphere model and then propagate those uncertainties through that atmospheric model. Although motivated in part by the then-upcoming Mars Science Lander mission, the focus of this project was on development of risk analysis methods for future entry, descent, and landing (EDL) missions. The project ultimately focused on the quantification and propagation of uncertainty in the distribution of dust in the Mars atmosphere, which is a major driver of the atmospheric dynamics and, consequently, any prospective EDL trajectory for a future Mars lander mission.

Over the first two years of this project, Dr. Balch had been trained in probabilistic uncertainty quantification and response surface methods. However, upon reaching NASA in the third year of the project, he quickly discovered that the data on dust loading did not support a purely probabilistic representation. This realization forced him to explore new ways of representing uncertainty: specifically, Dempster-Shafer theory and probability bounds analysis. What he found was that insisting on a probabilistic representation of epistemic uncertainty in the dust loading would cause an analyst to under-predict the uncertainty in atmospheric density profiles by a factor of two! 

Here is a paper summarizing the project. A much longer summary detailing the motivations and methods involved can be found in Dr. Balch's dissertation.