Statistical Experimental Design and Modeling for Complex Data

The ability to handle complex data is essential for new research findings and business success today. With increased complexity, data can either be difficult to collect with designed experiments or be difficult to analyze with statistical models. Both kinds of difficulties are addressed in this dissertation.The first part of this dissertation (Chapter 2 and 3) addresses the issue of complex data collection by considering two design of experiment problems. In chapter 2, we consider Bayesian A-optimal design problem under a hierarchical probabilistic model involving both quantitative and qualitative response variables. The objective function was derived and an efficient optimization algorithm was developed. In chapter 3, we consider the A/B-testing problem and propose a novel discrepancy-based approach for designing such an experiment. As the numerical examples show, the A/B-testing experiments designed in this way achieve better group balance and parametric estimation results.In the second part of this dissertation (Chapter 4 and 5), we focus on analyzing complex data with Gaussian process (GP) models. Gaussian process model is widely used for analyzing data with highly nonlinear relationships and emulating complex systems. In Chapter 4, we apply and extend GP model to analyze the in-cylinder pressure data resulted from experiments on a newly-developed dual fuel engine. The resulted model incorporates different data types and achieves good prediction accuracy. In Chapter 5, a generalized functional ANOVA GP model is proposed to tackle the difficulty resulted from high-dimensional feature space, and we develop an efficient algorithm for building such a model from the perspective of multiple kernel learning. The proposed approach outperforms traditional MLE-based GP models on both computational efficiency and prediction accuracy