Frame theory in directional statistics

Abstract

Distinguishing between uniform and non-uniform sample distributions is a common problem in directional data analysis; however for many tests, non-uniform distributions exist that fail uniformity rejection. By merging 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.

References in corpus (3)

• Spontaneous Patterning of Confined Granular Rods
• Principal arc analysis on direct product manifolds
• Random Tight Frames

Cited by in corpus (8)

• Minimization of the Probabilistic p-frame Potential
• Tight p-fusion frames
• Random Tight Frames
• Signal reconstruction from the magnitude of subspace components
• Probabilistic frames: An overview
• Signal Analysis based on Complex Wavelet Signs
• Preconditioning filter bank decompositions using structured normalized tight frames
• Exact Bayesian Inference for the Bingham Distribution