Reflection-asymmetric shapes of the atomic nucleus are relevant to nuclear stability, nuclear spectroscopy, nuclear decays and fission, and the search for new physics beyond the standard model. CP violation in the standard model is too weak to be responsible for the observed matter-antimatter asymmetry. Beyond standard model theories require additional source of CP violation, which could be found if non-zero atomic electric dipole moment (EDM) is observed. The nuclear quantity that induces the atomic EDM is the Schiff moment, which is enhanced in octupole-deformed odd-mass or odd-odd nuclei where parity doublets exist. This calls for two tasks: First, a global survey of octupole-deformed even-even nuclei to determine the nuclear regions with strong octupole instability; second, Schiff moment calculations in the odd-mass and odd-odd in the vicinity of strongly octupole-deformed even-even nuclei. The calculated Schiff moments will then help us determine the best candidates for atomic EDM measurements. These two tasks constitute the first part of this dissertation.The tool of choice for a large scale calculation on the entire nuclear landscape is nuclear DFT. Within the DFT framework, the Skyrme HFB method will be used to perform calculations in this dissertation. Although nuclear DFT is a powerful tool, it lacks the ability to provide quality uncertainty estimates for its predictions. In the second part of this dissertation, we explore several Bayesian machine learning techniques to further increase the predictive power of nuclear DFT, and to provide full Bayesian uncertainty quantification for DFT predictions.
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