Bayesian hierarchical methods for non-standard compositional data

Holland, Catherine (2025) Bayesian hierarchical methods for non-standard compositional data. PhD thesis, University of Glasgow.

Abstract

Compositional data take the form of parts of some whole, consisting of sets of non-negative components. Compositional data can appear as proportions, percentages, general non negative values or counts. The inherent characteristics of compositional data, i.e. non negativity and the constraint to some total, pose unique challenges for traditional statistical techniques. Compositional data arise across many real-world applications such as health, environmental, forensic, financial and sports science. Further challenges occur when compositional data also include other advanced data challenges such as multilevel hierarchical structure, non-smooth time series or a spatial structure.

The main technique in the literature to overcome the complexities of compositional data is to transform the components from the simplex (the sample space of compositional data) into Euclidean space (the standard statistical space) using a log-ratio transformation. Once transformed, standard statistical models can be applied. However, while this transformation is powerful, it is not always suitable in practice. There are many features commonly found within compositional data that prohibit log-ratio transformations. For example, when compositional data contain zeros, the log-ratios become undefined. Similarly, when the components contain missing values, some or all of the log-ratio transformations may not produce sensible results. Lastly, when compositional data consist of counts, applying a log ratio transformation may discard information on how the total count may impact the variance and the possible values the counts can take. Thus, there is a need for frameworks that can handle compositional data containing these features, as well as addressing advanced data challenges.

This thesis presents novel Bayesian hierarchical frameworks designed to overcome the limitations of log-ratio transformations in these instances. We apply and evaluate our proposed frameworks to three applications of compositional data containing both a feature which prevents log-ratio transformations and an advanced data challenge. These include: compositional data containing many zeros and a multilevel hierarchical structure, applied to forensic elemental glass data; non-smooth time series containing a count structure and zero values, applied to COVID-19 variant counts; and compositional data with a spatial pattern containing zeros, applied to tree species proportions across a spatial grid. We assess the performance of our frameworks through both in-sample and out-of-sample predictive experiments, comparing with commonly used models. The results from the predictive experiments demonstrate the effectiveness of our approaches, highlighting their contribution to compositional data analysis and offering a robust alternative for handling real-world compositional data.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: H Social Sciences > HA Statistics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Supervisor's Name: Stoner, Dr. Oliver and Neocleous, Dr. Tereza
• Date of Award: 2025
• Depositing User: Theses Team
• Unique ID: glathesis:2025-85372
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 05 Aug 2025 13:43
• Last Modified: 05 Aug 2025 13:45
• Thesis DOI: 10.5525/gla.thesis.85372
• URI: https://theses.gla.ac.uk/id/eprint/85372