Keywords
Probability, Nested Dirichlet Process, Mathematics
Abstract
This body of research focuses on Bayesian nonparametric inference, in regards to an array of S-valued random variables. These random variables are assumed to take values in a complete and separable metric space and further have a particular symmetry property, row exchangeability.
The Nested Dirichlet Process is a particularly apt model for inference in such circumstances. However, calculating posterior distributions in this framework is exceedingly difficult, and become exponentially more complicated as sample size increases.
This research explores the method of using sequential imputation to calculate posterior distributions, providing a rigorous proof of the method’s suitability that had been missing in previous works.
Completion Date
2025
Semester
Fall
Committee Chair
Jason Swanson
Degree
Doctor of Philosophy (Ph.D.)
College
College of Sciences
Department
Mathematics
Format
Identifier
DP0029836
Document Type
Thesis
Campus Location
Orlando (Main) Campus
STARS Citation
Donald, Evan C., "The Nested Dirichlet Process And Applications To Nonparametric Bayesian Inference" (2025). Graduate Thesis and Dissertation post-2024. 439.
https://stars.library.ucf.edu/etd2024/439