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Elastic Functional Changepoint Detection of Climate Impacts from Localized Sources
Abstract: Functional data analysis (FDA) is an important research area, due to its broad applications across many disciplines where functional data is prevalent. An essential component in solving these problems is the registration of points across functional objects. Without proper registration the results are often inferior and difficult to interpret. The current practice in the FDA literature is to treat registration as a pre-processing step, using off-the-shelf alignment procedures, and follow it up with statistical analysis of the resulting data. In contrast, an elastic framework is a more comprehensive approach, where one solves for the registration and statistical inferences in a simultaneous fashion. Our goal is to use a metric with appropriate invariance properties, to form objective functions for alignment and to develop statistical models involving functional data. While these elastic metrics are complicated in general, we have developed a family of square-root transformations that map these metrics into simpler Euclidean metrics, thus enabling more standard statistical procedures. In this talk, we present a changepoint method for functional data which properly accounts for these types of invariances and demonstrate on simulated data and climate data from the eruption of Mt. Pinatubo in the Philippines in June 1991.
J. Derek Tucker is a Distinguished Member of the Technical Staff at Sandia National Laboratories and Adjunct Faculty at University of Illinois Urbana-Champaign. He received his B.S. in Electrical Engineering Cum Laude and M.S. in Electrical Engineering from Colorado State University in 2007 and 2009, respectively. In 2014 he received the Ph.D. degree in Statistics from Florida State University in Tallahassee, FL under the co-advisement of Dr. Anuj Srivastava and Dr. Wei Wu. He currently is leading research projects in the area of Bayesian model calibration and statistical functional modeling of optical emissions. His research is focused on pattern theoretic approaches to problems in image analysis, computer vision, and signal processing.
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