Taking chances with the sciences

The aim of this course is that the students learn how to combine graph theory and probability theory to infer graphical models from real-world data. In the course we will focus on Bayesian networks, which can for example be used to infer gene regulatory networks and protein pathways in systems biology research. After a very brief introduction to typical biological applications, we will consider Bayesian networks from a statistical perspective. As Bayesian networks bring together graph theory and probability theory, we will first discuss various graph theoretic concepts, before we can start modelling graphs statistically.

In this context we will also have to discuss the most important fundamentals of Bayesian Statistics. Finally, we will learn how to infer Bayesian networks from real-world data. Throughout the course we will use the statistical computing environment R to implement some of the discussed algorithms. Some more sophisticated R implementations will be made available.

Although graphical models, such as Bayesian networks, have recently become a very important and popular tool in the topical field of Systems Biology, these models are usually not discussed in classical Statistics courses.

Outline of the course

The five main topics, covered in this course, are:

• Introductions to Graphical Models, Bayesian Statistics and Bayesian networks.
• The Markov property, conditional independency relations, the concept of d-separation, equivalence classes of graphs.
• The BDe scoring metric for discrete Bayesian networks and the BGe scoring metric for Gaussian Bayesian networks.
• Practical graph inference with greedy search algorithms or Markov Chain Monte Carlo (MCMC) simulations.
• Dynamic Bayesian networks.

At the end of this course students are expected to be able to:

• translate applied and real-world problems into graphical models;
• interpret graphical models with respect to their conditional independency-properties;
• statistically model graphs;
• infer graphical models from real-world data

Assignment

Each student can choose between two options. Either he/she is evaluated based on a written report or he/she can take an oral exam of about 20 minutes. In the oral exam it will be tested whether all the concepts have been sufficiently understood. The topics of the reports are relatively flexible. The student could for example analyze some data from his/her own field with Bayesian networks and then write a paper about the applied methods and results. Alternatively, the student could write a report on a specific topic or give an overview to Bayesian network methodology.

Schedule

Here you will find the schedule.

More information

Ocasys