Grant: Discovery Grants Program - Individual

High dimensional spatial and temporal data are abundant in science and engineering research. They arise naturally from neural science, biology, environmental studies and many other scientific investigations. For example, the impact of climate change are evaluated using spatial or temporal data such as temperature and humidity. In addition, brain activities can be characterized by current density vectors defined at 6000 voxels located throughout the human brain. These brain vectors are then recorded through time in order to find significant patterns related to active thinking processes. In medical diagnosis, fetal stresses are also monitored by many correlated variability measures that are collected through time in order to make a timely decision to avoid severe brain damages. All the aforementioned research directions demand effective statistical modeling of complex high dimensional data.This proposal consists of three closely related proposed research directions that are designed to tackle different aspects of this challenging problem to model high-dimensional spatial and temporal data. The first is about clustering and classification of high dimensional complex data in order to divide them into homogenous groups so that they can be analyzed by statistical models. It also includes variable selection techniques for high dimensional categorical data also known as tensor data. The second approach is about approximate likelihood inference when the exact underlying likelihood is either unknown or untractable. Estimating the parameters of differential equations is also part of it. A high dimensional optimization and integration approach will also be proposed.