New Modeling and Bayes Inference for 3-D Orientations/Rotations and Equivalence Classes of Them Seminar

We provide a technical overview of a recent series of papers by Bingham, Qiu, Du, Nordman, and Vardeman concerning modeling and inference for 3-D orientations and equivalence classes of them. The work was first motivated by the analysis of crystal orientation data collected by materials scientists via electron backscatter diffraction and has also proved useful in biomechanics applications. Important new symmetric and non-symmetric parametric models have been developed, and an alternative view of some existing symmetric models has been exploited. Bayes methodology is highly effective and leads to geometrically interpretable inferences for both the symmetric and non-symmetric models. Nice technical "surprises" in the development have been the near-perfect frequentist calibration of the Bayes inferences and the practical hyper-efficiency of Bayes methodology in non-regular models. The modeling and inference methodology is tractable enough to provide useful inference in hierarchical (and other kinds of) modeling involving rotations.