Collaborative Research: Statistical Analysis of Partially Observed Shapes in Two Dimensions

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Classification of shapes has many important applications in a variety of fields. For example, anthropologists use shape classification on fossilized faunal teeth to reconstruct past environments and on variation in the shapes of stone tools to assess different technological strategies. Other applications include classification of plants based on the shape of their leaves and identification of shapes of tumors. While there are many statistical tools that can be used for classification, most methods are based on complete shapes with relatively few methods available for partially observed or incomplete shapes. This project focuses of the development of new statistical methodology, based on the ideas of multiple imputation, for the analysis of partially observed shapes.This project proposes as a starting point leveraging the ideas of nonparametric, hot-deck type multiple imputation to shapes that are defined by unlabeled points and/or functions, as opposed to shapes defined by landmarks where traditional methods of multiple imputation may be applied. The proposed method involves matching partially observed shapes to fully observed shapes, randomly choosing a fully observed donor shape among the shapes that are good matches for the partial shape, and then completing the partial shape with the unmatched part of the donor shape. A simulation study will be conducted to compare the relative merits of different partial matching methods. The imputation framework will be tested using teeth from the Family Bovidae, whose classification plays an important role in biological anthropology for identifying the taxa of specimens, which in turn is used to reconstruct paleoenvirnoments.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.