Degree Type


Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Stephen B. Vardeman

Second Advisor

Daniel J. Nordman


Investigating cubic crystalline structures of specimens is an important way to study properties of materials in text analysis. Crystals in metal specimens have internally homogeneous orientations relative to a pre-chosen reference coordinate system. Clusters of crystals in the metal with locally similar orientations constitute so-called "grains." The nature of these grains (shape, size, etc.) affects physical properties (e.g., hardness, conductivity, etc.) of the material. Electron backscatter diffraction (EBSD) machines are often use to measure orientations of crystals in metal specimens. However, orientations reported by EBSD machines are in truth equivalence classes of crystallographically symmetric orientations.

Motivated by the materials science applications, we formulate parametric probability models for "unlabeled orientation data." This amounts to developing models on equivalence classes of 3-D rotations. A Bayesian method is developed for inferencing parameters in the models, which is generally superior to large-sample methods based on likelihood estimation. We also proposed an algorithms for clustering equivalence classes of 3-D orientations. As we continue to work on this area, we found and studied an interesting class of Markov chains with state spaces partitions of a finite set. These Markov chains have some properties that make them attractive in their own right, and they are potentially helpful in Bayesian model-based clustering.


Copyright Owner

Chuanlong Du



File Format


File Size

73 pages