This talk discusses some recent developments on the following three research areas:
(1) Designs and Analysis of Experiments. Design and analysis of experiments is important for cost-efficiency and variation reduction in the experiments conducted in scientific researches and industrial processes. Although theories of factorial designs and methodologies in computer experiments have been well-developed in the past decades, some other experiments require special structure on their experimental plans that are yet fully investigated. In the first part of this talk, the theoretical structure and the construction of circulant orthogonal arrays are introduced. Such designs can be applied to the experiments in functional magnetic resonance imaging to enhance the estimation ability on the HRF signal peaks when compared to traditional sequences.
(2) Network Data Analysis. In the big data regime, analyses on new types of large-scale data, like network data, introduce new challenges to traditional statistical researches. Most methods in network analysis are originated from computer scientists and many are lack of statistical tests for verifications. In the second part of this talk, a new statistical approach on the network data analysis is introduced. It consists of an exploration step via graph coloring, a community detection step via scan statistic and a centrality verification step via focus degree centrality. The likelihood-based community detection method not only allows the users to analyze the structure of a network, but also the attribute information on both the nodes and the edges. The new focus degree centrality incorporates the information from the whole network, not just the neighboring nodes in the traditional centralities.
(3) Nature-inspired Metaheuristic Optimization. Parallel or distributed computing has been the future in the programming architecture, and nature-inspired metaheuristic algorithm is a common practice in engineering to search for optimal solutions in continuous domains via parallel computing. However, unlike most physical sciences, many solutions in mathematics and statistics fall in discrete domains. In the third part of this talk, a new metaheuristic method, called the Swarm Intelligence Based method, is introduced for the optimization in discrete domains. Both the standard framework and the later augmented version are discussed and several examples in experimental designs, community detection and change point analysis are shown for demonstration.
In the last part of this talk, some ongoing and future projects in the above three areas plus two additional research areas are introduced.