Apr 22

3:30 pm

## Split Models - An Extension of Graphical Models

### Soren Hojsgaard

Seminar

Aalborg University - Departments of Biometry & Informatics

Graphical models are convenient for representing the qualitative structure of association among variables in a complex domain. Vertices in a graph represent variables, edges between vertices represent possible associations, and absence of an edge between two vertices implies that these are conditionally independent given the remaining variables.

One deficiency of graphical models is that statements of the form "B and C are independent given A=1, but dependent when A=2" can not be embedded in graphical models.

Split models are an attempt to remedy this. Formally split models generalize graphical models. A split model is represented by a tree of graphs. The graph at the root represents the "overall" structure of association among the varibales in terms of conditional independencies. when conditioning on particular outcomes of some variables.

In the talk, split models will be motivated by practical examples. The main focus will be on the interpretation of graph trees. Some aspects of inference will be considered and an application to data concerning women and mathematics will briefly be described.