Date Available
2020
Year of Publication
2020
Degree Name
Doctor of Philosophy (PhD)
Document Type
Doctoral Dissertation
College
Arts and Sciences
Department/School/Program
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
Recommended Citation
Maraj, Aida, "Algebraic and Geometric Properties of Hierarchical Models" (2020). Theses and Dissertations--Mathematics. 71.
https://uknowledge.uky.edu/math_etds/71
Included in
Algebra Commons, Algebraic Geometry Commons, Discrete Mathematics and Combinatorics Commons, Statistics and Probability Commons
