Nordic Informatics Network in the Agricultural Sciences

Reasoning under Uncertainty in Agriculture: Bayesian networks and Graphical Models

Tune Landboskole, August 10-21 2003

Background

Within agricultural and other kinds of biological research many problems involving the need for reasoning without perfect knowledge are studied. Examples are numerous and includes for instance:

• The diagnostic problem in veterinary medicine: Based on more or less specific symptoms, the veterinarian must establish a diagnosis in terms of a specific diseases that the animal suffers from. If the symptoms are to vague, the veterinarian may take supplementary observations as for example laboratory analyses that may increase his belief in a specific disease. In many cases, however, certainty is never obtained.
• The diagnostic problem in plant protection: In case of plant diseases, the decision maker faces an analogous problem of identifying a plant disease based on on or more symptoms. In this case, however, the uncertainty about the weather conditions during the next days will increase the uncertainty concerning the need for treatment.
• The pregnancy test problem: If an animal is mated there is a certain probability that it is pregnant. If furthermore it does not show heat in the next cycle, our belief in pregnancy will increase, and later a positive pregnancy test will increase it further, but until the offspring is actually born there will be a slight uncertainty concerning the true state of the animal.
• The trouble shooting problem in agricultural engineering: If some kind of technical equipment (e.g. a feeding machine or a tractor) fails a number of tests are used in order to identify the cause. A well-structured test sequence is needed in order to identify the problem with a high degree of certainty at a low cost.

A common trait of the examples mentioned is that we try to identify the true state of some system. The problem is, however, that this state is not directly observable. Instead we observe some other variables which in some sense are correlated to the true state. Based on those indirect observations we try to make a conclusion concerning the true state.

Bayesian networks (or more generally, graphical models) provide an excellent framework for handling this kind of problems in a consistent way. During the recent years, several agricultural applications relying on this technique have been developed, and also from a theoretical point of view, the research area of graphical modeling is currently experiencing a burst. It is now one of the main areas of research in artificial intelligence.      

Aim of the course

The first objective of the course is to give the participants an overview of the basic principles for reasoning in graphical models. During the course, the principles will be emphasized through illustrative examples from agriculture and other biological sciences. 

An other objective is to introduce the participants to model building in practice through exercises and a minor project using a computer tool for graphical models. Therefore methods for estimation of the probability distributions used in such models are introduced.

After the course, the PhD students will be able to build graphical models of a biological or technical domain originating from their main project. They are familiar with the basic principles for reasoning including observation and entering of evidence, propagation and conclusion.

 Required knowledge

Basic statistical courses, including basic probability theory. Familiarity with computers at user level.

Topics and Key Words

This summer school will focus on the following main topics

• graphical modeling of biological systems by use of Bayesian networks and related techniques,
• estimation of probability distributions,
• implementation of the models on a computer,
• use of the resulting system for reasoning under uncertainty,
• learning from data (data mining)
• evaluation of the computed results

The material will be illustrated with various examples from agriculture and biology, and supplemented with guest lectures on related issues.

Throughout the course, the theory will be supplemented with exercises and computer assignments. At the end of the course, the students will work on a two-day project that involves both modeling and computing aspects.

The following key words describe the technical contents of the course.

• Causal networks.
• Probability calculus.
• Bayesian networks.
• Conditional independence, d-separation.
• Modeling with graphical networks: Methods, examples, tricks.
• Compilation: Triangulation, moralization, junction trees.
• Software for graphical models.
• Techniques for estimation of conditional probability distributions.
• Sensitivity analyses.

Scientifically responsible

Professor Finn Verner Jensen, Dr. Math., Department of Computer Science, Aalborg University, Denmark.

Organisational responsible

Associate Professor and head of the Dina Research School, Anders Ringgaard Kristensen, D.Sc., Department of Animal Science and Animal Health, Royal Veterinary and Agricultural University, Denmark.

External Lecturers

• Professor Serafín Moral, Department of Computer Science, University of Granada, Spain.
• Professor Linda van der Gaag, Institute of Information and Computing Sciences, Universiteit Utrecht, The Netherlands
• Chief Scientist Erik Jørgensen, Danish Institute of Agricultural Sciences, Denmark.

Refer to the appendices for presentation of the teachers.

Teaching methods

Lectures alternating with intensive use of computer exercises. The availablility of network connected computers is therefore essential for the benefit of the students. A small project is carried out by the students at the end of the course (individually or preferably in small groups).

Examination will be based on a written project report handed in at the end of the course in combination with an oral presentation. The number of credits proposed is 6 ECTS.

Author: phd@dina.kvl.dk. Updated: 11 oktober 2002