Document Type

Article

Publication Version

Published Version

Publication Date

2014

Journal or Book Title

Statistica Sinica

Volume

24

Issue

2

First Page

897

Last Page

917

DOI

10.5705/ss.2011.235

Abstract

For modeling orientation data represented as 3 × 3 rotation matrices, we develop a wrapped trivariate normal distribution (wTND) under which random rotations have simple geometric construction as symmetric errors about a mean. While of interest in its own right, the wTND also provides simple and effective approximations to the isotropic Gaussian distribution on rotations, with some advantages over approximations based on other commonly used models. We develop non-informative Bayes inference for the wTND via Markov Chain Monte Carlo methods that allow straightforward computations in a model where maximum likelihood is undefined. Credible regions for model parameters (including a fixed 3 × 3 mean rotation) are shown to possess good frequentist coverage properties. We illustrate the model and inference method with orientation data collected in texture analysis from materials science.

Comments

This article is from Statistica Sinica 24 (2014): 897, doi: 10.5705/ss.2011.235. Posted with permission.

Copyright Owner

Institute of Statistical Science, Academia Sinica

Language

en

File Format

application/pdf

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