Statistical methodology for multi-dimensional data

我是一名统计学家，与数学家、神经学家、神经学家和临床医生密切合作。 数据越来越复杂，统计分析变得越来越具有挑战性。医学图像、分子结构、传感器网络等都可以表示为点云数据、曲线曲面点云和定义在流形上的随机过程。 这些是高维数据的典型示例，难以可视化和捕获对象的真实特征。 数据的多维性质使数学和统计分析复杂化。 最近，拓扑学家提出了计算技术，用于提取高维数据的拓扑和几何特征。 在众多的统计方法中，函数数据分析是曲线点云数据分析的有效方法。 我的研究目标之一是建立一个统计模型，可以将医学图像数据，临床，生物学和心理测量随时间推移。 我的总体研究目标是通过应用计算拓扑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比较多发性硬化症患者，阿尔茨海默病患者和对照组中得到证明。

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.