Algebraic statistics

Summary

Algebraic statistics uses algebraic geometry and commutative algebra to study statistical models and procedures. Many models for discrete data are sets of probability vectors cut out by polynomial equations. Examples are independence models for contingency tables, graphical models and log-linear models. Tools such as polynomial ideals, Gröbner bases and algebraic varieties then give information on identifiability, maximum likelihood estimation and exact tests. A well-known example is the use of Markov bases, introduced by Persi Diaconis and Bernd Sturmfels, to sample tables with fixed margins.