Date of Award

Spring 5-15-2015

Degree Type

Thesis

Degree Name

M.S.

Degree Program

Mathematics

Department

Mathematics

Major Professor

Linxiong Li

Abstract

Modeling of compositional data is emerging as an active area in statistics. It is assumed that compositional data represent the convex linear mixing of definite numbers of independent sources usually referred to as end members. A generic problem in practice is to appropriately separate the end members and quantify their fractions from compositional data subject to nonnegative and unit-sum constraints. A number of methods essentially related to polytope expansion have been proposed. However, these deterministic methods have some potential problems.

In this study, a hierarchical Bayesian model was formulated, and the algorithms were coded in MATLABÒ. A test run using both a synthetic and real-word dataset yields scientifically sound and mathematically optimal outputs broadly consistent with other non-Bayesian methods. Also, the sensitivity of this model to the choice of different priors and structure of the covariance matrix of error were discussed.

Rights

The University of New Orleans and its agents retain the non-exclusive license to archive and make accessible this dissertation or thesis in whole or in part in all forms of media, now or hereafter known. The author retains all other ownership rights to the copyright of the thesis or dissertation.

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