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Timetable

This is tentative and subject to what people are interested in discussing, volunteers, etc.

Wk
Date
Topic
Presenter
Reading
1
24th Nov 2009 Introduction
Ideals and Varieties (slides here)
Robin Evans IVA - Chapter 1;
Drton, Sturmfels and Sullivant (2007)
2
1st Dec Groebner Bases Charles Doss IVA - Chapter 2
3
8th Dec Algebraic Inference for Contingency Tables Anna Klimova Diaconis and Sturmfels (1998)
 
Christmas Break
   
4
13th Jan Implicitization, Nullstellensatz (?) Alex Volfovsky IVA - Chapters 3, 4
5
20th Jan Rational Functions on Varieties collaborative IVA - Chapter 5
6
27th Jan Likelihood Inference - Discrete and Gaussian Models collaborative LAS - Chapter 2.1
7
3rd Feb Markov Bases collaborative LAS - Chapter 1.1-1.2
8
10th Feb Likelihood Inference collaborative LAS - Chapter 2.2-2.3
9
17th Feb      
10
24th Feb A geometric Buchberger algorithm for integer programming Rekha Thomas Thomas (1995)
11
3rd Mar      
12
10th Mar      
   
Spring Break
   

Meetings at 3:30pm on Tuesdays in Padelford C-301. This will change to Wednesdays, 3:30pm after Christmas.

 

Books

Algebraic Statistics (AS) - Pistone, Riccomagno & Wynn

Ideals, Varieties and Algorithms, Third Edition (IVA) - Cox, Little & O'Shea

Lectures on Algebraic Statistics (LAS) - Drton, Sturmfels & Sullivant

 

Papers

Cavender, J.A. and Felsenstein, J. (1987) - InvariantsĀ of phylogenies in a simple case with discrete states

Thomas, R.R. (1995) - A geometric Buchberger algorithm for integer programming

Diaconis, P. and Sturmfels, S. (1998) - Algebraic algorithms for sampling from conditional distributions

Drton, M. (2006) - Algebraic techniques for Gaussian models, Prague Stochastics

Allman, E.S. and Rhodes, J.A. (2006) - Phylogenetic invariants for stationary base composition

Drton, M. and Sullivant, S. (2007) - Algebraic statistical models

Drton, M., Sturmfels and Sullivant, S. (2007) - Algebraic factor analysis: tetrads, pentads and beyond

Allman, E.S. and Rhodes, J.A. (2008) - Phylogenetic ideals and varieties for the general Markov model

Drton, M. (2009) - Likelihood Ratio Tests and Singularities

Zwiernik, P. and Smith, J.Q. (2009) - The Geometry of Independence Tree Models with Hidden Variables

 

Links

SINGULAR - Software for automatic algebraic computations.

Laboratory for Mathematical and Computational Biology, UC Berkeley