Graphical Models and Inference  MT11

Overview of Lectures

These are the contents of 16 lectures in MT11. 

  1. Graphs and conditional independence
  2. Markov properties for undirected graphs
  3. Log-linear models
  4. Maximum likelihood in log-linear models
  5. Decomposability
  6. Junction trees
  7. Markov properties for directed acyclic graphs
  8. Bayesian networks and expert systems
  9. Probability propagation
  10. The multivariate Gaussian distribution
  11. Gaussian graphical models
  12. Decomposable and directed Gaussian graphical models 
  13. Graphical models for causal inference
  14. Estimation of (causal?) structure
  15. Bayesian graphical models
  16. 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


General course description.

Last updated:  Monday 28 November 2011Steffen L. Lauritzen