Author ORCID Identifier
0000-0002-4578-0026
Defense Date
2025
Document Type
Dissertation
Degree Name
Doctor of Philosophy
Department
Mathematical Sciences
First Advisor
Yanjun Qian, PhD
Second Advisor
Edward Boone, PhD
Third Advisor
Cheng Ly, PhD
Fourth Advisor
Mo Jiang, PhD
Abstract
Ultraviolet--visible (UV--Vis) spectroscopy produces high-dimensional signals that are strongly collinear, shift with concentration, and exhibit heteroskedastic, non-Gaussian noise. These features make supervised regression from spectra to ionic concentrations statistically challenging and limit the reliability of methods that assume linear structure or homoscedastic errors.
This dissertation develops two complementary frameworks for prediction and uncertainty quantification in UV--Vis spectroscopic regression: (1) frequentist stacked ensembles combined with distribution-free conformal prediction, and (2) Bayesian hierarchical modeling and Bayesian stacking. Together, they provide a unified view of model-based and distribution-free uncertainty across nickel and nickel--cobalt datasets.
The frequentist component builds ensembles of Functional Data Analysis (FDA), Principal Component Regression (PCR), and Partial Least Squares (PLS) learners. Three ensemble strategies---non-negative least squares stacking, Dirichlet-regularized stacking, and a piecewise ensemble---improve point prediction by exploiting complementary structure in the spectral representations. Uncertainty is quantified with Split Conformal, CV+, Jackknife, and Jackknife+, which deliver finite-sample valid prediction intervals without distributional assumptions. A new kernel-weighted nonexchangeable conformal method incorporates spectral similarity, enabling locally adaptive intervals when observations are not exchangeable.
The Bayesian component develops hierarchical FDA, PCR, and PLS models with priors tailored to smooth functional structure and likelihoods suited to positive, heteroskedastic targets. Posterior predictive distributions supply coherent probabilistic uncertainty, and Bayesian stacking combines models by maximizing expected predictive performance.
Developed on the nickel dataset and evaluated on the mixed nickel--cobalt data for robustness, the two frameworks deliver strong predictive accuracy and complementary forms of uncertainty: conformal methods guarantee distribution-free coverage, while Bayesian models provide full probabilistic structure and interpretability.
Rights
© The Author
Is Part Of
VCU University Archives
Is Part Of
VCU Theses and Dissertations
Date of Submission
12-12-2025