Year of Publication

2020

Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation

College

Arts and Sciences

Department

Mathematics

First Advisor

Dr. Uwe Nagel

Abstract

In this dissertation filtrations of ideals arising from hierarchical models in statistics related by a group action are are studied. These filtrations lead to ideals in polynomial rings in infinitely many variables, which require innovative tools. Regular languages and finite automata are used to prove and explicitly compute the rationality of some multivariate power series that record important quantitative information about the ideals. Some work regarding Markov bases for non-reducible models is shown, together with advances in the polyhedral geometry of binary hierarchical models.

Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2020.232

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