## Bayesian Analysis

### Bayes one-sample and one-way random effects analyses for 3-D orientations with application to materials science

#### 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.

#### Article information

Source
Bayesian Anal., Volume 4, Number 3 (2009), 607-629.

Dates
First available in Project Euclid: 22 June 2012

https://projecteuclid.org/euclid.ba/1340369857

Digital Object Identifier
doi:10.1214/09-BA423

Mathematical Reviews number (MathSciNet)
MR2551048

Zentralblatt MATH identifier
1330.62016

#### Citation

Bingham, Melissa A.; Vardeman, Stephen B.; Nordman, Daniel J. Bayes one-sample and one-way random effects analyses for 3-D orientations with application to materials science. Bayesian Anal. 4 (2009), no. 3, 607--629. doi:10.1214/09-BA423. https://projecteuclid.org/euclid.ba/1340369857