• additive models;
  • Bayesian networks;
  • bugs;
  • directed acyclic graphs;
  • Markov chain Monte Carlo;
  • measurement error models;
  • missing data;
  • mixed models;
  • penalized splines;
  • variational approximation;
  • variational inference;
  • vibes


Semiparametric regression models that use spline basis functions with penalization have graphical model representations. This link is more powerful than previously established mixed model representations of semiparametric regression, as a larger class of models can be accommodated. Complications such as missingness and measurement error are more naturally handled within the graphical model architecture. Directed acyclic graphs, also known as Bayesian networks, play a prominent role. Graphical model-based 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.