This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
Statistical design and analysis of experiments is an effective and commonly used tool in scientific discoveries. The rapid growth in technology and computing power has made available many complex experiments, such as those with branching factors and functional responses. It also poses many new challenges. The primary objective of this proposal is to develop a set of novel and efficient statistical methods to tackle the emerging challenges and thus accelerate discoveries in many disciplines that use experimental investigation. The research plan consists of two parts. The first part of the research focuses on design and analysis of experiments with branching and nested factors. In many complex experiments, some of the factors exist only within the level of another factor. Such factors are often called nested factors. A factor within which other factors are nested is called a branching factor. Design and analysis of experiments with branching and nested factors are crucial in many complex systems and have not received much attention in the literature. In the first part of this proposal, new classes of designs, theory, combinatorial and algorithmic construction strategies, and structured modeling are proposed that can take into account the branching and nested structure in a complex experiment and identify important factors effectively. The second part of the research focuses on the analysis of computer experiments with functional responses. Physical experiments can be expensive and time-consuming; thus, computer experiments have been widely used as economical alternatives. Many computer experiment responses are collected in a functional form. However, literature on modeling computer experiments with functional responses remains scarce as most of the existing modeling techniques focus on single outputs. Although there are some dimension reduction techniques for functional responses, they do not account for an important feature, the deterministic outputs, of computer experiments. To address this issue, a sequential technique is proposed, which provides an interpolating model. It also incorporates a novel iterative procedure and thus enjoys great computational efficiency.
The new class of designs, design theory, combinatorial and algorithmic construction methods, and structured models proposed in this research appears to be the first systematic investigation of experiments with branching and nested factors. They can open new avenues for studying problems that energize both theoretical and applied research. The proposed sequential modeling technique for computer experiments with functional responses takes into account the special features in computer experiments and enjoys great computational efficiency. It is an innovative concept which can lead to new research in functional data analysis. Both methods are readily applicable to a variety of scientific fields, such as electronic packaging, biomechanical engineering design, wildfire control, and influenza modeling.
