Dupuis, PaulMao, Yixiang2021-08-0420202020-09-092020-11Mao, Yixiang. 2020. Formulation and properties of a divergence used to compare probability measures without absolute continuity and its application to uncertainty quantification. Doctoral dissertation, Harvard University Graduate School of Arts and Sciences.28092743https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37368875This thesis develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and exploit a representation as an infimum convolution of optimal transport cost and relative entropy. We include examples of computation and approximation of the divergence, and its applications in uncertainty quantification in discrete models and Gauss-Markov models.application/pdfenconvex dualityKL divergencemodel uncertaintyoptimal transport theoryrelative entropyMathematicsInformation scienceThesis or Dissertation2021-08-040000-0002-8295-8911