Bayesian methods for structure detection in analysis of object data

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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.