  Optimization via simulation (OvS) procedures that assume the simulation
inputs are generated from the real-world distributions are subject to the risk
of selecting a suboptimal solution when the distributions are substituted with
input models estimated from finite real-world data -- known as input model
risk. Focusing on discrete OvS, this paper proposes a new Bayesian framework
for analyzing input model risk of implementing an arbitrary solution, $x$,
where uncertainty about the input models is captured by a posterior
distribution. We define the $\alpha$-level risk set of solution $x$ as the set
of solutions whose expected performance is better than $x$ by a practically
meaningful margin $(>\delta)$ given common input models with significant
probability ($>\alpha$) under the posterior distribution. The user-specified
parameters, $\delta$ and $\alpha$, control robustness of the procedure to the
desired level as well as guards against unnecessary conservatism. An empty risk
set implies that there is no practically better solution than $x$ with
significant probability even though the real-world input distributions are
unknown. For efficient estimation of the risk set, the conditional mean
performance of a solution given a set of input distributions is modeled as a
Gaussian process (GP) that takes the solution-distributions pair as an input.
In particular, our GP model allows both parametric and nonparametric input
models. We propose the sequential risk set inference procedure that estimates
the risk set and selects the next solution-distributions pair to simulate using
the posterior GP at each iteration. We show that simulating the pair expected
to change the risk set estimate the most in the next iteration is the
asymptotic one-step optimal sampling rule that minimizes the number of
incorrectly classified solutions, if the procedure runs without stopping.
