# Relevant textbooks:

## 1. "Lectures on Algebraic Statistics" Drton, Sturmfels, Sullivant

List of seminar topics and relevant sections of the book:- Markov bases: hypothesis tests for contingency tables: sec.1.1
- Markov bases of hierarchical log-linear models: sec.1.2
- Graphical models/ conditional independence models: Parts of Chp 3

## 2. "Markov Bases in Algebraic Statistics" Aoki, Hara, Takemura (downloadable from Springerlink!)

(**Note from the book's preface:__"This book is intended for statisticians with minimal backgrounds in algebra. "__**)

List of seminar topics and relevant sections of the book:

- Exact Tests for Contingency Tables and Discrete Exponential Families: Chp 1
- Markov Chain Monte Carlo Methods over Discrete Sample Space: Chp 2
- Algebra background (with view toward Markov bases!): Chapters 3 and 4

# Problems and suggested related papers (can be found on the arXiv):

- (topic A) Generating Markov sub-bases efficiently
- "Markov Chains, Quotient Ideals, and Connectivity with Positive Margins", Chen Dinwoodie and Yoshida
****Recommended reading in preparation for Rudy's visit in April* - "Markov bases and subbases for bounded contingency tables", Fabio Rapallo, Ruriko Yoshida
- "Connecting tables with zero-one entries by a subset of a Markov basis", Hisayuki Hara, Akimichi Takemura
- "Running Markov chain without Markov basis", Hisayuki Hara, Satoshi Aoki, Akimichi Takemura
- ..

- "Markov Chains, Quotient Ideals, and Connectivity with Positive Margins", Chen Dinwoodie and Yoshida
- (topic A) Using algebraic statistics (Markov bases; implicitization) for model selection or factorial design
- "Algebraic Statistics in Model Selection", Luis David Garcia (2004)
- "Bayesian model choice and information criteria in sparse generalized linear models", Rina Foygel, Mathias Drton
- "Markov basis for design of experiments with three-level factors", Satoshi Aoki, Akimichi Takemura
- "Design and analysis of fractional factorial experiments from the viewpoint of computational algebraic statistics", Satoshi Aoki, Akimichi Takemura
- ..

- (topic B) Understanding the geometry of graphical mixture models in biology (phylogenetcs)
- "Phylogenetic Algebraic Geometry", Nicholas Eriksson, Kristian Ranestad, Bernd Sturmfels, Seth Sullivant

( arXiv:math/0407033 , overview paper, points to open problems and several topics) - "Geometry of the Kimura 3-parameter model", Marta Casanellas, Jesus Fernandez-Sanchez
- "On the ideals of equivariant tree models", Jan Draisma, Jochen Kuttler
- " Bounded-rank tensors are defined in bounded degree", Jan Draisma, Jochen Kuttler
- "The space of phylogenetic mixtures for equivariant models", Marta Casanellas, Jesus Fernandez-Sanchez, Anna Kedzierska
- "Identifiability of Large Phylogenetic Mixture Models", John A. Rhodes, Seth Sullivant
- "When Do Phylogenetic Mixture Models Mimic Other Phylogenetic Models?", Elizabeth S. Allman, John A. Rhodes, Seth Sullivant
- (topic B) Parameter identifiability problems
- "Binary hidden Markov models and varieties", Andrew J. Critch
- "Identifying Causal Effects with Computer Algebra", Luis David GarcĂa-Puente, Sarah Spielvogel, Seth Sullivant (2010)
- "Parameter identifiability in a class of random graph mixture models", Elizabeth S. Allman, Catherine Matias, John A. Rhodes
- "Identifiability of parameters in latent structure models with many observed variables", Elizabeth S. Allman, Catherine Matias, John A. Rhodes
- "Identifying evolutionary trees and substitution parameters for the general Markov model with invariable sites", Elizabeth S. Allman, John A. Rhodes
- ..