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

PDF

Identifier

DP0029836

Document Type

Thesis

Campus Location

Orlando (Main) Campus

Subjects

Mathematical statistics--Research; Bayesian statistical decision theory--Mathematical models; Nonparametric statistics--Asymptotic theory; Inference--Mathematical models; Multiple imputation (Statistics)

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