Importance Sampling and its Optimality for Stochastic Simulation Models

We consider the problem of estimating an expected outcome from a stochastic simulation model. Our goal is to develop a theoretical framework on importance sampling for such estimation. By investigating the variance of an importance sampling estimator, we propose a two-stage procedure that involves a regression stage and a sampling stage to construct the final estimator. We introduce a parametric and a nonparametric regression estimator in the first stage and study how the allocation between the two stages affects the performance of the final estimator. We analyze the variance reduction rates and derive oracle properties of both methods. We evaluate the empirical performances of the methods using two numerical examples and a case study on wind turbine reliability evaluation.Comment: 37 pages, 6 figures, 2 tables. Accepted to the Electronic Journal of Statistic

Computationally Efficient Reliability Evaluation With Stochastic Simulation Models.

Thanks to advanced computing and modeling technologies, computer simulations are becoming more widely used for the reliability evaluation of complex systems. Yet, as simulation models represent physical systems more accurately and utilize a large number of random variables to reflect various uncertainties, high computational costs remain a major challenge in analyzing the system reliability. The objective of this dissertation research is to provide new solutions for saving computational time of simulation-based reliability evaluation that considers large uncertainties within the simulation. This dissertation develops (a) a variance reduction technique for stochastic simulation models, (b) an uncertainty quantification method for the variance reduction technique, and (c) an adaptive approach of the variance reduction technique. First, among several variance reduction techniques, importance sampling has been widely used to improve the efficiency of simulation-based reliability evaluation using deterministic simulation models. In contrast to deterministic simulation models whose simulation output is uniquely determined given a fixed input, stochastic simulation models produce random outputs. We extend the theory of importance sampling to efficiently estimate a system's reliability with stochastic simulation models. Second, to quantify the uncertainty of the reliability estimation with stochastic simulation models, we can repeat the simulation experiment multiple times. It, however, multiplies computational burden. To overcome this, we establish the central limit theorem for the reliability estimator with stochastic simulation models, and construct an asymptotically valid confidence interval using data from a single simulation experiment. Lastly, theoretically optimal importance sampling densities require approximations in practice. As a candidate density to approximate the optimal density, a mixture of parametric densities can be used in the cross-entropy method that aims to minimize the cross-entropy between the optimal density and the candidate density. We propose an information criterion to identify an appropriate number of mixture densities. This criterion enables us to adaptively find the importance sampling density as we gather data through an iterative procedure. Case studies, using computationally intensive aeroelastic wind turbine simulators developed by the U.S. Department of Energy (DOE)'s National Renewable Energy Laboratory (NREL), demonstrate the superiority of the proposed approaches over alternative methods in estimating the system reliability using stochastic simulation models.PhDIndustrial and Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/120894/1/yjchoe_1.pd