  Studies on simulation input uncertainty often built on the availability of
input data. In this paper, we investigate an inverse problem where, given only
the availability of output data, we nonparametrically calibrate the input
models and other related performance measures of interest. We propose an
optimization-based framework to compute statistically valid bounds on input
quantities. The framework utilizes constraints that connect the statistical
information of the real-world outputs with the input-output relation via a
simulable map. We analyze the statistical guarantees of this approach from the
view of data-driven robust optimization, and show how the guarantees relate to
the function complexity of the constraints arising in our framework. We
investigate an iterative procedure based on a stochastic quadratic penalty
method to approximately solve the resulting optimization. We conduct numerical
experiments to demonstrate our performance in bounding the input models and
related quantities.
