Bayesian methods for structure detection in analysis of object data

如今，图像、函数数据、随机集、形状、图形和树等复杂数据对象通常用于表示观测中存在的信息。贝叶斯方法非常适合于检测隐藏在这些复杂数据集下的有意义的结构。该结构可以以稀疏的形式出现，将许多参数值设置为类似于零的空值，或者通过使相邻的值相等，从而有效地减少要处理的参数的数量。本项目将为建立关于控制目标数据分布的参数的先验分布以及以有效方式计算所产生的后验分布提供明确的指导方针。研究的主要思想是使用一个辅助随机过程来控制对象数据之间的联系。该项目将多尺度建模、特征共享、多重测试、随机几何、机器学习和非参数贝叶斯范式等不同概念结合在一起，并将这些不同的概念综合为分析对象数据的强大方法。该项目还促进了利用结构细节(如条件共轭)的计算策略的发展，从而提供了快速和准确的计算方法。该项目开发的方法将为在数据集合中寻找结构提供基础，在天文学、医学、工程、金融和其他各种领域都有广泛的应用。这项研究将有助于以更准确和高效的方式处理天文图像，从而有助于识别遥远的超新星遗迹和其他天体中的事件。这项研究还将对医学成像产生重大影响，因为它提供了一种准确处理敏感器官扫描的方法，几乎不会暴露在有害射线中。该项目将以研究生咨询的形式影响人力资源开发。该项目将有适合本科生研究项目的子项目。将努力让代表不足的群体的学生参与进来，以促进多样性。

Complex data objects such as images, functional data, random sets, shapes, graphs and trees are nowadays commonly used to represent information present in observations. Bayesian methods are well suited for detecting meaningful structures hidden underneath these complex data sets. The structure may come in the form of sparsity, setting many parameter values to a null value like zero, or by making adjacent values equal, thus effectively reducing the number of parameters to handle. This project will provide definitive guidelines for constructing prior distributions on the parameters controlling the distributions of object data, and for computing the resulting posterior distributions in an efficient manner. The main idea of the research is to use an auxiliary stochastic process to control ties in object data. The project connects diverse concepts such as multi-scale modeling, feature sharing, multiple testing, random geometry, machine learning and nonparametric Bayesian paradigm, and synthesizes these different concepts into a powerful approach for analyzing object data. The project also stimulates the development of computing strategies that exploit structural niceties such as conditional conjugacy, thus providing fast and accurate computational approaches.This project develops methodologies that will provide a foundation for finding structures in collections of data, with a wide range of applications in astronomy, medical sciences, engineering, finance, and various other fields. The research will help process astronomical images in a more accurate and efficient manner, and thus help identify events in distant supernova remnants and other astronomical bodies. The research will also have a significant impact in medical imaging, by providing a method of accurate processing of scans of sensitive organs with very little exposure to harmful rays. The project will impact human resource development in the form of graduate student advising. The project will have subprojects that will be suitable topics for undergraduate research projects. Efforts will be made to involve students from under-represented groups to promote diversity.