My current research is focused on Experimental design theory, group testing designs and high-dimensional data analysis.
(1) Experimental design theory. Most statistical research is concerned how to efficiently extract information from data, but design problems are considered how to collect most informative data. With my coauthors, I have three papers in this area. The first paper (JSPI2014) studies the robust design for logit and probit models, which can be applied in the sensitivity and safety analysis for the pyrotechnics experiments. Our designs have good efficiency for parameter estimation under the two models and provide minimal probability bias under the wrong one. The second paper (JSPI2016) considers quadratic models with random block effects, which can be applied in paired data experiments, such as the experiments on eyes or feet. The third paper (JSPI2020) theoretically characterize optimal designs for binary response experiments with multivariate covariates, such as logit or probit models, which can be applied on flammability experiments.
(2) Group testing. Group testing (a.k.a. pool testing) plays an important role in prevalence estimation and case diagnosis. I am particularly interested in the design problems for the prevalence estimation. In group testing study, samples from individuals are pooled and tested as a single unit. Thus, group testing technique aggregates individual information and thus reduces number of trials and saves cost. Group testing is widely used in areas such as epidemiology, genetics, public health, food safety, and drug development. When the number of individuals is extremely high and the prevalence is relatively low, such as environmental monitoring data, group testing is extremely efficient. Traditional group testing designs only have a single group size. With my coauthors, my first paper (JRSSB2017) in this area, which introduces techniques from optimal design of experiments into group testing community, provides optimal group testing designs with multiple group sizes for precise prevalence estimation under uncertain testing error rates. Based on the first work, my second and third papers (Sinica2020, EJS2021) provide efficient group testing designs incorporating practical issues, such as budget constraints, dilution effects, and multiple trials.
(3) High-dimensional data analysis. In the recent years, I also focus on dimension reduction in high-dimensional data analysis. With my coauthors, my first paper (JABES2021) provides a two-stage functional canonical correlation analysis (CCA) to test independence between two series of image data. In the first stage, we project the images to lower dimensional subspaces considering spatial structures; in the second stage, we apply the conventional CCA on projected images. We show that our two-stage CCA outperforms the conventional CCA and the EOF-CCA which is frequently applied in teleconnection studies in climate research. my second paper (JMA2021) focus on the asymptotic properties of the Kronecker envelope principal component analysis (PCA), which has many successful applications on single-particle cryogenic electron microscopy image analysis. We show that the Kronecker envelope PCA is asymptotically more efficient than the conventional PCA in some scenarios.