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

Course schedule - Bayesian approach