• Statistical Uncertainty Analysis for Stochastic Simulation (collaborate with Barry L. Nelson, Russell R. Barton)

When we use simulation to evaluate the performance of a stochastic system, the simulation often contains input models estimated from real-world data. There is both simulation and input uncertainty in the system performance estimates. For the independent input data, we proposed rigorous approaches to quantify the impact of both input and simulation estimation uncertainty on system performance estimate: the metamodel-assisted bootstrapping approach and a Bayesian framework. Both approaches can make effective use of the simulation budget and provide good finite-sample performance.

• Marketing Analytics (collaborate with Edward C. Malthouse, Vijay Viswanathan and Su Jung Kim)

The emergence of modern information and communication technologies including social media platforms, mobile devices and applications (apps) offers a multiplicity of touch points to engage customers with particular brands. By analyzing customer data from a well-known coalition loyalty program called the Canadian Air Miles Reward Program, we glean insights about how customer engagement through mobile apps affects the customer purchasing behavior. We employ a vector-autoregressive (VAR) model to account for the dynamic interactions among non-purchase customer engagement behaviors (i.e., app usage), purchase and consumption. The information extracted from our study can help marketers adjust their marketing strategy and improve their marketing effectiveness. 

• Stochastic Kriging (collaborate with Barry L. Nelson, Jeremy Staum)

  Kriging and stochastic kriging are commonly used machine learning approaches. Based on simulation outputs or observations at a small set of input models, they can be used to predict the system mean response as a function of the independent variables. Since the correlation function plays a critical role in both kriging and stochastic kriging models, we studied various correlation functions in both spatial and frequency domains and analyzed their impact on prediction accuracy.

• Approximate Dynamic Programming in Supply Chain Systems (collaborate with Diego Klabjan)

To study the solution methodogies for general multi-echelon systems, approximate dynamic programming was used to obtain appropriate shipping policies. Since the computation time can increase prohibitively for complex supply chain systems, various parallel algorithms based on message passing interface were proposed to speed up the computation time.

• Signal Processing for Nondestructive Test (collaborate with Imad L. Al-Qadi, Douglas L. Jones)

Ground penetrating radar (GPR) with various frequency antennaes is used to obtain comprehensive under-surface information about railroad track substructure, pavements and bridges. To automatically process massive amounts of ultra-wideband signals collected from GPR, we proposed various analysis approaches to analyze the data from different objects. They demonstrated good performance.

• Damage and Fracture with Peridynamics (collaborate with Florin Bobaru)

The peridynamic formulation is a novel reformulation of the classical continuous mechanics theory and has strong ties with molecular dynamics models. This method leads to a meshfree implementation able to successfully model complicated fracture and fragmentation patterns at impact, spallation, etc. To simulate shock waves, the Flux-Corrected Transport technique was implemented in the peridynamic method leading to the Peridynamic Flux-Corrected Transport algorithm. This method can efficiently eliminate the high frequency oscillation behind the shock wave fronts and overcome limitations in the Finite Element Flux-Corrected method.