Simulator-Enabled Conformal Prediction

In the past few decades, every-growing computation power has increased the potential to model complex

processes. A range of scienti?c research has leveraged this advancement to develop simulators that enable high-resolution views into variability in complex systems, which can then be utilized to quantify uncertainty in the conclusions drawn from real, observed data. At the same time, the ?eld of conformal prediction has created a collection of frameworks that construct ?nitely-valid prediction regions applicable to many types of models and rely on only a weak assumption of exchangeability of observations. The 

exibility of conformal inference makes it a natural ?t for use in conjunction with the output of complex simulation models.

Hence, this thesis presents work to extend conformal prediction to simulation models. The specific approach presented is sufficiently flexible to work in a wide range of spaces where prediction regions can be useful. Emphasis is placed on the extension to functional data. The proposed prediction regions are geometrically understandable and possess many desirable statistical and practical properties. This thesis examines the application of the proposed method to stylized examples that highlight the method's properties and to a real world example that de?nes prediction regions for multidimensional summary functions that

characterize tropical cyclone convection structure.