Nordic Informatics Network in the Agricultural Sciences

Bayesian approach - when and why (not)

Structural equations modeling and Bayesian analysis

Häme Polytechnic, Mustiala Faculty of Agriculture, Finland, July 30 - August 10, 2007

Background

This hybrid course will cover two different, but complimentary, aspects of statistical modelling. Structural equations modelling deals with testing hypotheses about the topological structure of multivariate statistical models; i.e. hypotheses concerning how variables are linked together in the form of a causal hypothesis concerning direct and indirect effects. Bayesian analysis deals with the way that uncertainties (such as from prior information, or unknown parameters), coded in the form of a probability density, are integrated with subsequent observations in order to estimate and test statistical hypotheses. Since these two topics deal with quite different aspects of the modelling enterprise they are complementary and, together, provide a more complete understanding of statistical modelling.

Topics and Key Words

The course will provide both a theoretical background and practical instruction on the application of these methods.

Part I: Structural Equations

• The logic of causal inference
• Independence, partial independence and d-separation
• D-separation tests
• Exploratory methods using d-separation
• Maximum likelihood estimation of SEM
• Modelling latent variables
• Inferential tests based on maximum likelihood
• Nested models

Part II: Bayesian analysis and hierarchical models

• What is probability?
• Bayesian inference
• Graphical Models
• Hierarchical Models
• MCMC
• Missing data and prediction

Target audience

PhD students and other researchers, primarily within the agricultural and biological sciences, who require advanced knowledge in these areas.

Required knowledge & prerequisites.

We assume that participants have a basic knowledge of statistical methods and are familiar with personal computers working in a Windows environment.

Scientifically responsible

Hannu Rita, Dept. of Forest Resource Management, P.O. Box 27 (Latokartanon-kaari 7), FI-00014 University of Helsinki;
E-mail: hannu.rita@helsinki.fi

Teaching methods

Lectures alternating with intensive use of computer exercises. The availability of required software (EQS and OpenBUGS) is essential.

Suggested references

• Shipley, B. 2000. Cause and correlation in biology: A user’s guide to path analysis, structural equations, and causal inference. Cambridge University Press.
• Gelman, A. and Hill, J. 2006. Data analysis using regression and multi-level/hierarchical models. Cambridge University Press.

Examination

Examination (pass/no-pass) 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 is 6 ECTS.

Author: phd@dina.kvl.dk. Updated: 29 marts 2007