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Dissertation Defense: Yejin Choi

A view of Cockins Hall from below
June 23, 2025
10:00 am - 12:00 pm
CH 440 Conference Room

Dissertation Defense: Yejin Choi
 
Title: Analysis of Spatial Functional Data with Phase Variations and Planar Curves
 
Abstract: Understanding spatial patterns in complex data objects such as functional data and shapes of planar curves is challenging but crucial in many scientific fields. This dissertation introduces statistical frameworks for analyzing spatial dependence and performing spatially-informed local summarization in spatially indexed functional data and shapes.
 
The first part introduces a new approach for locally summarizing spatially dependent shape data. we define a shape trace-variogram to compute spatially-weighted averages and covariances of shapes. These quantities allow for local summaries that integrate spatial dependence in observations. In particular, spatially-weighted covariance matrices are used to perform localized principal component analysis, enabling visualization of dominant spatial shape variation. We demonstrate this method on the shapes of cell nuclei in histopathology images, capturing regional variations in nuclear shape while accounting for spatial proximity.
 
The second part develops a general framework for assessing spatial dependence in functional data and planar curves. We introduce five trace-variograms tailored to specific types of variation—amplitude and phase for functional data, and shape, orientation-and-shape, and size-and-shape for curves. These are incorporated into a second-order summary statistic based on the inhomogeneous K-function, enabling formal assessment of spatial dependence. Applications to sea salinity profiles and breast cancer histopathology images highlight the importance of modeling distinct sources of variation in spatially distributed functional and shape data. 
 
Advisor: Sebastian Kurtek