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title:
Probabilistic frames, fusion frames and applications in statistics
name:
Ehler
first name:
Martin
location/conference:
NOKO11
abstract:
Distinguishing between uniform and non-uniform sample distributions on the unit sphere is a common problem in directional data analysis; however for many tests, non-uniform distributions exist that fail uniformity rejection. To characterize such distributions, we merge directional statistics with frame theory. We find that probabilistic tight frames yield non-uniform distributions that minimize directional potentials, leading to failure of uniformity rejection for the Bingham test. Finally, we apply our results to model patterns found in granular rod experiments, and we discuss modifications to address samples on the Grassmannian manifold.