Bayesian inference for polycrystalline materials

Polycrystalline materials, such as metals, are composed of heterogeneously oriented crystals. Observed crystal orientations modelled a sample from an orientation distribution function (ODF), which determines variety material properties and is therefore great interest to practitioners. Observations consist quaternions, four-dimensional unit vectors reflecting both rotation single crystal. Thus, ODF must account for known symmetries well satisfy the length constraint. A popular method estimating ODFs nonparametrically symmetrized kernel density estimation. However, disadvantages this approach include difficulty in interpreting results quantitatively, quantifying uncertainty ODF. We propose use mixture symmetric Bingham distributions flexible parametric model, inferring number components, weights, scale location parameters based on data. Furthermore, our Bayesian allows structured quantification interest. discuss details sampling methodology conclude with analyses various datasets, interpretations interest, comparison estimation methods.