Campus Units
Industrial and Manufacturing Systems Engineering, Statistics
Document Type
Article
Publication Version
Accepted Manuscript
Publication Date
2009
Journal or Book Title
Journal of the American Statistical Association
Volume
104
Issue
488
First Page
1385
Last Page
1397
DOI
10.1198/jasa.2009.ap08741
Abstract
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. We 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. We 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. We 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.
Copyright Owner
American Statistical Association
Copyright Date
2009
Language
en
Recommended Citation
Bingham, Melissa Ann; Nordman, Daniel J.; and Vardeman, Stephen B., "Modeling and Inference for Measured Crystal Orientations and a Tractable Class of Symmetric Distributions for Rotations in Three Dimensions" (2009). Industrial and Manufacturing Systems Engineering Publications. 146.
https://lib.dr.iastate.edu/imse_pubs/146
Included in
Industrial Engineering Commons, Statistics and Probability Commons, Systems Engineering Commons
Comments
This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association in 2009, available online: http://www.tandfonline.com/10.1198/jasa.2009.ap08741