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。 数据更加复杂正成为一种趋势，因此统计分析可能极具挑战性。医学图像、分子结构和传感器网络可以表示为定义在流形上的点云数据、曲线曲面点云和随机过程。 这些都是高维数据的典型例子，其中很难可视化和捕捉对象的真实特征。这些数据的多维性质使数学和统计分析变得复杂。 最近，拓扑学家提出了提取高维数据的拓扑和几何特征的计算技术。在众多的统计方法中，函数数据分析对于曲线点云数据分析是非常有用的。 我的研究目标之一是建立一个统计模型，该模型可以包含医学图像数据、临床、生物和心理测量数据。 我的总体研究目标是通过应用计算拓扑学和函数数据分析来增强多元统计技术。 我的研究方法的有效性将在多发性硬化症患者、阿尔茨海默病患者和对照组的比较中得到证明。

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.