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2009 Bayes one-sample and one-way random effects analyses for 3-D orientations with application to materials science
Melissa A. Bingham, Daniel J. Nordman, Stephen B. Vardeman
Bayesian Anal. 4(3): 607-629 (2009). DOI: 10.1214/09-BA423

Abstract

We consider Bayes inference for a class of distributions on orientations in 3 dimensions described by $3 \times 3$ rotation matrices. Non-informative priors are identified and Metropolis-Hastings within Gibbs algorithms are used to generate samples from posterior distributions in one-sample and one-way random effects models. A simulation study investigates the performance of Bayes analyses based on non-informative priors in the one-sample case, making comparisons to quasi-likelihood inference. A second simulation study investigates the behavior of posteriors for some informative priors. Bayes one-way random effect analyses of orientation matrix data are then developed and the Bayes methods are illustrated in a materials science application.

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Melissa A. Bingham. Daniel J. Nordman. Stephen B. Vardeman. "Bayes one-sample and one-way random effects analyses for 3-D orientations with application to materials science." Bayesian Anal. 4 (3) 607 - 629, 2009. https://doi.org/10.1214/09-BA423

Information

Published: 2009
First available in Project Euclid: 22 June 2012

zbMATH: 1330.62016
MathSciNet: MR2551048
Digital Object Identifier: 10.1214/09-BA423

Rights: Copyright © 2009 International Society for Bayesian Analysis

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Vol.4 • No. 3 • 2009
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