Statistical Analysis of Partially Observed Shapes in Two Dimensions with Applications in Biological Anthropology

• Activity Number: 79 - Functional Data Analysis: Methods and Applications
• Type: Contributed
• Date/Time: Sunday, July 28, 2019 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Gregory Matthews* and Ofer Harel and Juliet Brophy and George Thiruvathukal
• Companies: and Dept of Statistics, U of Connecticut and Louisiana State University and Loyola University Chicago
• Keywords: Shapes; Missing data

Abstract

Statistical analysis of two-dimensional shapes is an important problem in a wide array of fields. When shapes are fully observed there are many proposed methods for analyzing these shapes. However, less well studied are statistical methods for the analysis of shapes that are only partially observed. Past research on partially observed shapes has primarily been performed using landmarks to define shapes. Often, in these settings, traditional missing data techniques such as multiple imputation can be applied. When shapes are not defined by landmarks, but rather are viewed in a functional data analysis framework, dealing with partially observations becomes more challenging. In this setting, traditional missing data techniques are not applicable. This research aims to develop novel methodologies for analyzing partially observed shapes in two dimensions by extending the concepts of multiple imputation to partially observed shapes in two-dimensions. We apply our methods to the classification of bovid teeth based on the shape of the occlusal surface of a tooth, which is important to biological anthropoloigists when performing paleoenvironmental reconstructions.