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The paper examines the relative errors (REs) of quantile estimators of various stochastic models under different asymptotic regimes. Depending on the particular limit considered and the Monte Carlo method applied, the RE may be vanishing, bounded, or unbounded. We provide examples of these possibilities. 

Plausible inference is a growing body of literature that treats stochastic simulation as a gray box when structural properties of the simulation output performance measures as a function of design, decision or contextual variables are known. Plausible inference exploits these properties to allow the outputs from values of decision variables that have been simulated to provide inference about output performance measures at values of decision variables that have not been simulated; statements about the possible optimality or feasibility are examples. Lipschitz continuity is a structural property of many simulation problems. Unfortunately, the all-important—and essential for plausible inference—Lipschitz constant is rarely known. In this paper we show how to obtain plausible inference with an estimated Lipschitz constant that is also derived by plausible inference reasoning, as well as how to create the experiment design to simulate. 

This paper studies the allocation of simulation effort in a ranking-and-selection (R&S) problem with the goal of selecting a system whose performance is within a given tolerance of the best. We apply large-deviations theory to derive an optimal allocation for maximizing the rate at which the so-called probability of good selection (PGS) asymptotically approaches one, assuming that systems’ output distributions are known. An interesting property of the optimal allocation is that some good systems may receive a sampling ratio of zero. We demonstrate through numerical experiments that this property leads to serious practical consequences, specifically when designing adaptive R&S algorithms. In particular, we observe that the convergence and even consistency of a simple plug-in algorithm designed for the PGS goal can be negatively impacted. We offer empirical evidence of these challenges and a preliminary exploration of a potential correction.