In this article, the authors report on their examination of the precision of current data modelling techniques and their development of a new statistical methodology for analyzing electron backspatter diffraction data.
Electron backscatter diffraction (EBSD) is a technique used in materials science to study the microtexture of metals, producing data that measure the orientations of crystals in a specimen. The authors examine the precision of such data based on a useful class of distributions on orientations in three dimensions (as represented by 3×3 orthogonal matrices with positive determinants). Although such modeling has received attention in the statistical literature, the approach taken typically has been based on general “special manifold” considerations, and the resulting methodology may not be easily accessible to nonspecialists. The authors take a more direct modeling approach, beginning from a simple, intuitively appealing mechanism for generating random orientations specifically in three-dimensional space. The resulting class of distributions has many desirable properties, including directly interpretable parameters and relatively simple theory. They investigate the basic properties of the entire class and one-sample quasi-likelihood–based inference for one member of the model class, producing a new statistical methodology that is practically useful in the analysis of EBSD data. This article has supplementary material online. (Published Abstract Provided)