Neural Networks can perform poorly when the training label distribution is heavily imbalanced, as well as when the testing data differs from the training distribution. In order to deal with shift in the testing label distribution, which imbalance causes, we motivate the problem from the perspective of an optimal Bayes classifier and derive a prior rebalancing technique that can be solved through a KL-divergence based optimization. This method allows a flexible post-training hyper-parameter to be efficiently tuned on a validation set and effectively modify the classifier margin to deal with this imbalance. We further combine this method with existing likelihood shift methods, re-interpreting them from the same Bayesian perspective, and demonstrating that our method can deal with both problems in a unified way. The resulting algorithm can be conveniently used on probabilistic classification problems agnostic to underlying architectures. Our results on six different datasets and five different architectures show state of art accuracy, including on large-scale imbalanced datasets such as iNaturalist for classification and Synthia for semantic segmentation. Please see https://github.com/GT-RIPL/UNO-IC.git for implementation.