The Statistics Seminar speaker for Wednesday, Sept. 9. 2020 is Armin Schwartzman. Schwartzman's research encompasses theoretical and practical aspects of statistical signal and image analysis in a variety of scientific applications. These include spatio-temporal and high-dimensional data analysis, geometric statistics and smooth Gaussian random fields, with applications in biomedicine, the environment, neuroscience, genetics and cosmology. Armin Schwartzman received his bachelor's and master's degrees in electrical engineering from the Technion - Israel Institute of Technology and the California Institute of Technology; and his PhD in Statistics from Stanford University. He was an R&D engineer at Rockwell Semiconductor and Biosense Webster, and has held faculty positions in Biostatistics at Harvard University and Statistics at North Carolina State University. He is now Professor at the University of California, San Diego, with a joint position between Biostatistics and the Halicioglu Data Science Institute.
Title: Coverage Probability Excursion (CoPE) Sets for Spatial Localization of Important Effects
This talk will be held via Zoom, with a link and password to the talk shared to the SDS community via email.
Abstract: Spatial functional data, for example in climate (2D) and neuroimaging (3D) studies, often ask the question: where are the important effects? Traditionally, especially in neuroimaging, this question has been answered via null hypothesis testing, assuming that the signal is sparse. But what if the signal is not sparse? Rather than testing for significance, we propose to directly estimate the spatial regions where the signal is above a certain importance threshold. The uncertainty in the estimates is then captured by a nested pair of spatial confidence regions, defined in such a way that the true excursion set is bounded with a given confidence. Given repeated noisy observations on a fine grid, asymptotic coverage probabilities may be determined using the Gaussian kinematic formula or via a multiplier bootstrap. As examples, the method is used to determine regions of substantial warming in North America in the 21st century, and to determine regions of high activation in task fMRI.