# Reading seminar

## Meets most Tuesdays at 2:30pm

## Location: 327 Thomas (and, occasionally, 320 Thomas; see schedule)

The particular topics are determined based on participants' interests in algebraic statistics in general. Part of the plan is to discover interesting open problems - and solve them!

* Check out the reading list (link above!). * There will be two main topics:

- (topic A) Open problems in Markov bases: hypothesis tests for contingency tables, hierarchical log-linear models.
- (topic B) Graphical mixture models: phylogenetics, parameter identifiability.

*(We will keep the schedule flexible; but please do sign up early to lead a reading session.)*

# Schedule

Date + Location |
Lead reader presenting |
Topic |

8 January(320 Thomas) |
Sonja Petrovic and Despina Stasi | Organizational meeting (and reading of an introductory/overview paper on Metropolis-Hastings algorithm) |

15 January 327 Thomas |
Sonja | Overview of topics A and B. |

29 January327 Thomas |
Despina Stasi | Generating Markov bases dynamically for p1 random graph models |

5 February327 Thomas |
Group | A "What is...?" session. Question 1: What is a fiber for the independence model? Question 2: Perform the random walk using a Markov basis on this fiber. Question 3: What is a geberuc `fiber' of a polynomial map? What does it mean for the parameters to be identifiable? |

12 February(320 Thomas) |
Vishesh Karwa | Markov bases applied to various problems Discussion about using lattice basis to make a connected chain? |

19 February327 Thomas |
Guido Montufar | Restricted Boltzmann machine |

26 February??? Thomas (meet on 4th floor of Thomas if no seminar room available!) |
Group discussion | What is a tropical variety? How do you use tropical approach to compute the dimension of an algebraic variety? --inspired by model dimension discussion of last week-- |

12 March(320 Thomas) |
Guido Montufar | Discrete Restricted Boltzmann Machine |

28 March (THU!)320 Thomas |
Jason Morton | open problem introduction.. |

9 April (320 Thomas) |
Vishesh Karwa | Combinatorial problems for MLE consistency |

16 April327 Thomas |
Ruriko Yoshida (Univeristy of Kentucky Statistics) |
tbd - open problem discussion |

22 April, 1pm (MON!)327 Thomas |
Julia Chifman (Department of Cancer Biology, Wake Forest University School of Medicine) |
This talk will be on Monday, because J.Chifman is also giving a talk at the Math Bio seminar on Tuesday 4/23. Title: Identifiability of Species Phylogenies Under the Coalescent Model
The inference of the evolutionary history of a collection of organisms based on the information contained in their DNA sequences is a problem of fundamental importance in evolutionary biology. The abundance of DNA sequence data arising from genome sequencing projects has led to significant challenges in the inference of these phylogenetic relationships. Among these challenges is the inference of the evolutionary history of a collection of species based on DNA sequence information from several distinct genes sampled throughout the genome. One of our goals is the identifiability of model parameters, which is one of the fundamental questions that must be answered when formulating any statistical model. We show that given a set of aligned DNA sequences, the species tree topology is identifiable for a specific set of substitution models.
Abstract: |

??30 April327 Thomas |
tbd | tbd |