Degree Type

Dissertation

Date of Award

2006

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Alicia Carriquiry

Second Advisor

Wolfgang Kliemann

Abstract

When the orientation of an object lies in a space of non-zero curvature usual distributions of probability cannot be used to describe its directions. One of such spaces is the Stiefel manifold. We focus on a probability distribution defined on that space, the matrix Langevin distribution. Classical and Bayesian methods of estimation of the parameter of the distribution are discussed. As the dimension of the Stiefel manifold increases, the more complicated the estimation process becomes given the complexity of the functions to be evaluated. A method is given that efficiently parameterizes the elements of the singular value decomposition of the parameter of the matrix Langevin distribution in terms of generalized Euler angles. How to implement that parameterization in the context of Bayesian estimation is shown. The methodology is illustrated with a dataset on trace element concentrations in bullet tips from the Federal Bureau of Investigations.

DOI

https://doi.org/10.31274/rtd-180813-159

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu

Copyright Owner

Gabriel Camano-Garcia

Language

en

Proquest ID

AAI3229054

File Format

application/pdf

File Size

110 pages

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