Algebraic Statistics for Computational Biology

Profesor: Lior Pachter, Departamento de Matemática de la Universidad de California, Berkeley

Primer cuatrimestre 2005

Prerrequisitos:

No prerequisite in biology or statistics.

What should be required is some mathematical maturity, and some knowledge

of algebra. An understanding of computational algebra at the level, of

say, Cox, Little O'Shea would be great. This will be a course primarily

for mathematicians.

Programa:

1. Statistics: Statistical models for discrete data. Linear models and toric models. Expectation maximization. Markov models. Graphical models.

2. Computation: Tropical arithmetic and dynamic programing. Sequence alignment. Polytopes. Trees and metrics. Software.

3. Algebra: Varieties and Gröbner bases. Implicitization. Maximum likelihood estimation. Tropical geometry. The tree of life and other tropical varieties.

4. Genomes. The data. The questions. Statistical models for a biological sequence. Statistical models of mutation.

Bibliografía:

Algebraic statistics for computational biology, edited by Lior Pachter and Bernd Sturnfels.

Modalidad: El Prof. Pachter iniciará el curso el 21 de marzo y dará cinco clases de dos horas de duración durante las dos primeras semanas. Luego regresará a principios de junio para cerrar el curso. En el interín se continuará con dos clases semanales de apoyo a cargo de otros profesores, preferentemente participantes del curso.