**Graphical Models and Inference MT11**

**Overview of Lectures**

These are the contents of 16 lectures in MT11.

- Graphs and conditional independence
- Markov properties for undirected graphs
- Log-linear models
- Maximum likelihood in log-linear models
- Decomposability
- Junction trees
- Markov properties for directed acyclic graphs
- Bayesian networks and expert systems
- Probability propagation
- The multivariate Gaussian distribution
- Gaussian graphical models
- Decomposable and directed Gaussian graphical models
- Graphical models for causal inference
- Estimation of (causal?) structure
- Bayesian graphical models
- Bayesian graphical models

Most of the topics discussed can be found in similar form in at least one of the following books:

Cowell, R. G., Dawid, A. P., Lauritzen, S. L. and Spiegelhalter, D.
J. (1999) *Probabilistic Networks and Expert Systems*.
Springer-Verlag, New York.

Edwards, D. (2000). *Introduction to Graphical Modelling* (2nd
ed). Springer-Verlag, New York.

Lauritzen, S. L. (1996). *Graphical Models*. Oxford University
Press, Oxford

Whittaker, J. (1990). *Graphical Models in Applied Multivariate
Statistics*. Wiley, Chicester.

You might also find my Aalborg lecture notes helpful. Many others have, even though they are somewhat dated, originally written in 1979.

S. L. Lauritzen. *Lectures on Contingency Tables.* Univ. Cop.
Inst. Math. Stat., 1979. *2nd ed.* Aalborg University Press 1982.
*3rd ed.* Department of Mathematics, Aalborg 1989.
Electronic
edition 2002 (pdf).

In 2006 I gave lectures at the summerschool at Saint Flour, France. My overheads for those lectures are here. Currently I intend to write proper lecture notes for this course. An incomplete draft of these is available here, and you might find these helpful as well.

For graph-theoretic concepts, see either Lauritzen (1996) or the first chapter in

Bollobas, B. (1998). *Modern Graph Theory*. Springer, New York

Last updated: Monday 28 November 2011. Steffen L. Lauritzen