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Activity Number: 192 - Contributed Poster Presentations: Section on Statistics and the Environment
Type: Contributed
Date/Time: Monday, July 30, 2018 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistics and the Environment
Abstract #329899
Title: Inferential Techniques for Persistent Homology
Author(s): Richard Ross* and Nicole Lazar and Lynne Seymour and Thomas Mote
Companies: University of Georgia and University of Georgia and University of Georgia and University of Georgia
Keywords: Persistent Homology; Topological Data Analysis; Inference; Morse Filtration; Climate

Persistent Homology continues to grow as a modern way to analyze the shape of data by exploiting principles from topology while adding understanding from statistical foundations. As this area continues to grow, there is an increasing demand for sound inferential methodology. We present here some tools useful for performing inference on persistence diagrams which help to preserve known spatial and temporal structure in the data. These methods are applied to climate data, analyzing atmospheric waves which contribute greatly to climate trends in the Northern Hemisphere. This involves use of sequential Morse filtrations to help preserve the structure while still capturing the true homology at each time point. The analysis shows the relationship between exploratory and inferential investigations of the data, using some both known and emerging tools for inference. We also highlight future directions for this type of inference, as well as enumerating the utility of said inference as it relates to climatological data.

Authors who are presenting talks have a * after their name.

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