  In predictive modeling with simulation or machine learning, it is critical to
accurately assess the quality of estimated values through output analysis. In
recent decades output analysis has become enriched with methods that quantify
the impact of input data uncertainty in the model outputs to increase
robustness. However, most developments are applicable assuming that the input
data adheres to a parametric family of distributions. We propose a unified
output analysis framework for simulation and machine learning outputs through
the lens of Monte Carlo sampling. This framework provides nonparametric
quantification of the variance and bias induced in the outputs with
higher-order accuracy. Our new bias-corrected estimation from the model outputs
leverages the extension of fast iterative bootstrap sampling and higher-order
influence functions. For the scalability of the proposed estimation methods, we
devise budget-optimal rules and leverage control variates for variance
reduction. Our theoretical and numerical results demonstrate a clear advantage
in building more robust confidence intervals from the model outputs with higher
coverage probability.
