A Factor-Based Bayesian Framework for Risk Analysis in Stochastic Simulations.

Simulation is commonly used to study the random behaviors of large-scale stochastic systems with correlated inputs. Since the input correlation is often induced by latent common factors in many situations, to facilitate system diagnostics and risk management, we introduce a factor-based Bayesian framework that can improve both computational and statistical efficiency and provide insights for system risk analysis. Specifically, we develop a flexible Gaussian copula-based multivariate input model that can capture important properties in the real-world data. A nonparametric Bayesian approach is used to model marginal distributions, and it can capture the properties, including multi-modality and skewness. We explore the factor structure of the underlying generative processes for the dependence. Both input and simulation estimation uncertainty are characterized by the posterior distributions. In addition, we interpret the latent factors and estimate their effects on the system performance, which could be used to support diagnostics and decision making for large-scale stochastic systems. Our approach is supported by both asymptotic theory and empirical study.