Advancements on the Interface of Computer Experiments and Survival Analysis

Design and analysis of computer experiments is an area focusing on efficient data collection (e.g., space-filling designs), surrogate modeling (e.g., Gaussian process models), and uncertainty quantification. Survival analysis focuses on modeling the period of time until a certain event happens. Data collection, prediction, and uncertainty quantification are also fundamental in survival models. In this dissertation, the proposed methods are motivated by a wide range of real world applications, including high-performance computing (HPC) variability data, jet engine reliability data, Titan GPU lifetime data, and pine tree survival data. This dissertation is to explore interfaces on computer experiments and survival analysis with the above applications.

Chapter 1 provides a general introduction to computer experiments and survival analysis. Chapter 2 focuses on the HPC variability management application. We investigate the applicability of space-filling designs and statistical surrogates in the HPC variability management setting, in terms of design efficiency, prediction accuracy, and scalability. A comprehensive comparison of the design strategies and predictive methods is conducted to study the combinations' performance in prediction accuracy.

Chapter 3 focuses on the reliability prediction application. With the availability of multi-channel sensor data, a single degradation index is needed to be compatible with most existing models. We propose a flexible framework with multi-sensory data to model the nonlinear relationship between sensors and the degradation process. We also involve the automatic variable selection to exclude sensors that have no effect on the underlying degradation process.

Chapter 4 investigates inference approaches for spatial survival analysis under the Bayesian framework. The Markov chain Monte Carlo (MCMC) approaches and variational inferences performance are studied for two survival models, the cumulative exposure model and the proportional hazard (PH) model. The Titan GPU data and pine tree survival data are used to illustrate the capability of variational inference on spatial survival models. Chapter 5 provides some general conclusions.