{"data":{"id":"10.6084/m9.figshare.1332458","type":"dois","attributes":{"doi":"10.6084/m9.figshare.1332458","prefix":"10.6084","suffix":"m9.figshare.1332458","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Chuanlong Du","affiliation":[],"nameIdentifiers":[]},{"name":"Nordman, Daniel J.","nameType":"Personal","givenName":"Daniel J.","familyName":"Nordman","affiliation":[],"nameIdentifiers":[]},{"name":"Vardeman, Stephen B.","nameType":"Personal","givenName":"Stephen B.","familyName":"Vardeman","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Bayesian Inference for a New Class of Distributions on Equivalence Classes of 3-D Orientations With Applications to Materials Science"}],"publisher":"Taylor \u0026 Francis","container":{},"publicationYear":2015,"subjects":[{"subject":"Developmental Biology"},{"subject":"Mathematics"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Mathematics","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Biological Sciences"},{"subject":"Immunology"},{"subject":"FOS: Clinical medicine","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Clinical medicine","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Ecology"},{"subject":"FOS: Biological sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Biological sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Earth and Environmental Sciences"},{"subject":"Cell Biology"}],"contributors":[],"dates":[{"date":"2015-03-11","dateType":"Created"},{"date":"2015-03-11","dateType":"Updated"},{"date":"2015","dateType":"Issued"}],"language":null,"types":{"ris":"DATA","bibtex":"misc","citeproc":"dataset","schemaOrg":"Dataset","resourceType":"Dataset","resourceTypeGeneral":"Dataset"},"relatedIdentifiers":[{"relationType":"IsSupplementTo","relatedIdentifier":"10.1080/00401706.2015.1017610","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":["7476027 Bytes"],"formats":[],"version":null,"rightsList":[{"rights":"Creative Commons Attribution 4.0 International","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc-by-4.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"Experiments in materials science investigating cubic crystalline structures often collect data which are in truth \u003ci\u003eequivalence classes\u003c/i\u003e of crystallographically symmetric orientations. These intend to represent how lattice structures of particles are orientated relative to a reference coordinate system. Motivated by a materials science application, we formulate parametric probability models for “unlabeled orientation data.” This amounts to developing models on equivalence classes of 3-D rotations. We use a flexible existing model class for random rotations (called uniform-axis-random-spin models) to induce probability distributions on the equivalence classes of rotations. We develop one-sample Bayesian inference for the parameters in these models, and compare this methodology to some likelihood-based approaches. We also contrast the new parametric analysis of unlabeled orientation data with other analyses that proceed as if the data have been preprocessed into honest orientation data. On-line supplementary materials are also available, providing additional computational 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