This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
Dimension reduction plays an essential role in reducing the complexity of data so that the most useful information in data can be successfully extracted. Most existing dimension reduction methods are developed under the assumption that the data are independent. Consequently, they may be inefficient and sometimes even inappropriate for analyzing spatial/temporal data which are often naturally correlated. The proposed research intends to fill in this gap by developing inverse regression based dimension reduction methods for data arising from three different types of spatial/temporal processes: spatial point processes, recurrent event processes and quantitative spatial processes. Specific goals of the project include 1) developing general frameworks and methods for conducting dimension reduction for both univariate and multivariate spatial point processes and 2) generalizing these methods to the cases of recurrent event processes and quantitative spatial processes. Special attentions will be given when the dimension of the response is also high. In addition, the PI will also develop computationally efficient analytical tools such as second-order analysis for the modeling of massive recurrent event process data.
With the fast development of modern data collection technologies, especially with the increased availability of more accurate Global Positioning System and Geographical Information System, large-scale spatial, temporal and spatial-temporal data have become rapidly available in recent years. Many of these data are massive and highly complex in nature, posing unprecedented challenges to data analysis. The proposed research will develop efficient statistical tools that can be used to analyze such data. The PI will collaborate closely with field scientists from various disciplines to apply these tools to solve real-life problems that have motivated this research. Specific goals of these collaborations includes, but are not limited to, 1) improving the understanding of tropical forestry diversity, 2) better assessing the health effects of air pollution on asthmatic children and 3) providing more accurate spatial predictions of US watershed characteristics such as discharges and fluxes. Key educational components of the project include providing interdisciplinary statistical trainings to students especially minority students at both the graduate and undergraduate levels and helping three local high schools improve their AP Statistics teaching.
