Title: Improving Neural Network Accuracy and Calibration Under Distributional Shift with Prior Augmented Data . Abstract: Neural networks have proven successful at learning from complex data distributions by acting as universal function approximators. However, neural networks are often overconfident in their predictions, which leads to inaccurate and miscalibrated probabilistic predictions. The problem of overconfidence becomes especially apparent in cases where the test-time data distribution differs from that which was seen during training. We propose a solution to this problem by seeking out regions in arbitrary feature space where the model is unjustifiably overconfident, and conditionally raising the entropy of those predictions towards that of the Bayesian prior on the distribution of the labels. Our method results in a better calibrated network and is agnostic to the underlying model structure, so it can be applied to any neural network which produces a probability density as an output. We demonstrate the effectiveness of our method and validate its performance on both classification and regression problems by applying it to the training of recent state-of-the-art neural network models.