I will talk about some recent methodologies to understand and quantify the impact of data in relation to optimization and simulation. In the first part of the talk, we create a new framework to statistically compare data- driven stochastic optimization approaches, especially regarding the issue of separation or integration between the “data-driven” step and the optimization step. Our results show that the performance ordering of various approaches depends on whether the model class of distributions covers the ground-truth distribution, and is completely opposite in these two cases in terms of stochastic dominance. In the second part, we develop new methodologies to quantify and reduce uncertainty for over-parameterized neural networks, especially addressing its “training” uncertainty in addition to the standard data noise. We create a new approach, which we call the procedural-noise-correcting predictor, to measure the training uncertainty and, by combining it with low-computation inference techniques from simulation, we demonstrate how to quantify overall statistical uncertainty in neural network with a minimal amount of retraining effort.