Wand, M. P., Semiparametric regression and graphical models, Centre for Statistical and Survey Methodology, University of Wollongong, Working Paper 18-08, 2008, 32p.
Semiparametric regression models that use spline basis functions with penalisation have graphical models representations. This link is more powerful than previously established mixed model representations of semiparametric regression since a bigger class of models can be accommodated. Complications such as missingness and measurement error are more naturally handled within the graphical models architecture. Directed acyclic graphs, also known as Bayesian networks, play a prominent role. Graphical modelsbased Bayesian “inference engines”, such as BUGS and VIBES, facilitate fitting and inference. Underlying these are Markov chain Monte Carlo schemes and recent developments in variational approximation theory and methodology.