Data-driven simulation modeling, uncertainty quantification, and optimization

Abstract

In this thesis, we address various decision-making problems with Monte Carlo simulation. Characterizing a simulation model (or input model), representing real-world randomness, is a key ingredient in simulation analysis. Even if we specify a family of input distributions well, the estimated input model is uncertain due to the finite length of historical data. This uncertainty affects the output evaluated by simulation. Such a potential risk often called as input uncertainty or input model risk in the simulation literature. Each chapter of this dissertation considers the different decision-making contexts, but they share the input uncertainty as a common issue.

In Chapters 2 and 3, we consider simulation modeling having a complex dependence structure. Chapter 2 suggests a data-driven input modeling based on the statistical method, ensemble copula coupling (ECC), under the presence of large input data. We can borrow the dependence structure of historical data and exploit it as a dependence model for the input model. We demonstrate the statistical convergences (consistency and asymptotic normality) of ECC to both input and simulation outputs with empirical process theory. Furthermore, we apply smooth bootstrap and subsampling to quantify input uncertainty and provides its theoretical justification.

In Chapter 3, we consider a high-dimensional correlated input. We focus on the Normal-to-Anything (NORTA), which allows flexible multivariate dependence modeling and is easy-to-sample. However, modern applications often face high-dimensional situations (large dimension and not-so-large input data size). Under this setting, the existing methods often fail or are inefficient to recover the underlying parameter, so it is not applicable. Our work fills this gap by introducing regularization-based estimators, and we solve efficiency issue arising when we apply it to simulation analysis.

In the last chapter, we study a discrete optimization via simulation (OvS) with input uncertainty. Our formulation aims to select the best alternatives hedging against the common input uncertainty. Especially, we suggest a novel robust solution, Selection of the Most Probable Best, and investigate several efficient simulation methods to find this solution. For this, we adopt an optimal budget allocation scheme (OCBA), and we derive an optimality condition for sampling policy, which minimizes the false selection probability.