Organizers

Some important facts

Program

The program of the initial phase of the seminar that we will cover is:

SESSION 1

A glimpse of history

The main subjects

Prerequisities

Tools for computing

A primer example: Discrete Markov Chain

SESSION 2

Part I - A Brief Review of Probability
Basic Notions
Random Variables and their Distributions
Expectation, Variance and Covariance
Limits Theorems
Part II - The Language and Ambient for Statistical Computing R
Data types, Basic Operators and Variables
Some built-in functions
Simulating Random Variables with R
Weak Law, Strong Law, and Central Limit Theorem with R

SESSION 3

Varieties

Ideals

Grobner Bases

Computational Algebra

Proyective Space and Proyective Varieties

SESSION 4

Conditional Independence

Conditional Independence Models

Primary Decomposition

Primary Decomposition of CI ideals

SESSION 5

Statistical Models

Parameter Estimation

Hypothesis Testing

R Exercises

Bayesian Statistics

R Exercises

SESSION 6

Design of Experiments

Design

Computation of Ideal of points

The Grobner Fan and applications

2-levels Design Systems of Reliability

Bibliography

  • Billingley, P., (1994), Probability and Measure, Third Edition.
  • Casella G. and Berger, (2000), Statistical Inference, Second Edition.
  • Cox, D., Little, J. and Oshea, D., (2015), Ideals Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commmutative Algebra. Fourth Edition, Springer.
  • Gareth, J., Witten, D., Hastie, T., and Tibshirani R. (2017), An introduction to Statistical Learning with applications in R, Springer.
  • R Core Team, R: A language and environment for statistical computing,R Foundation for Statistical Computing, 2019.
  • Sullivant, S., (2010), Algebraic Statistics, Note of Class.
  • Watanabe, S. (2009), Algebraic Geometric and Statistical Learning Theory, Cambridge Press.

Contact

If you want to know more about this seminar, please let us know: