Statistical methodology for multi-dimensional data

我是一名统计学家，与数学家、正畸医生、神经科医生和临床医生密切合作。

I am a statistician and work closely with mathematicians, orthodontists, neurologists, and clinicians. It is becoming a trend that data are more complex and so statistical analysis can be extremely challenging. Medical images, molecular structures, and sensor networks, can be expressed as point cloud data, curves and surfaces point cloud, and random process defined on manifolds. These are typical examples of high dimensional data where it is difficult to visualize and capture the true features of objects. The multidimensional nature of the data complicates mathematical and statistical analyses. Recently, topologists have come up with computational techniques for extracting topological and geometrical features of high dimensional data. Among many statistical methods, functional data analysis is useful for curve point cloud data analysis. One of my research aims is to build a statistical model that can incorporate medical image data, clinical, biological, and psychological measurements taken over time. My overall research goal is to enhance the multivariate statistical techniques by applying computational topology and functional data analysis. The effectiveness of my research methodologies will be demonstrated in comparing Multiple Sclerosis patients, Alzheimer patients and controls.