An Invitation to Algebraic Statistics

Algebraic statistics has flourished in recent years as a branch of applied algebraic geometry. This field is fundamentally connected to and driven by methods from statistics, computational algebraic geometry, and combinatorics. The algebraic methods have applications to statistical models where standard computational tools do not scale well, for example, phylogenetics, social networks, and graphical models. In turn, some of the open problems suggest developments on the computational frontier.

This talk will survey a brief history of recent developments in the field. We will focus on the problem of constructing Markov moves for exponential family models. The idea will be illustrated on an example for a random graph model used in the social network literature. Time permitting, we will also briefly discuss the problem of parameter identifiability in graphical models.