A comparison of hybrid strategies for Gibbs sampling in mixed graphical models

Graphical models represent a network approach to describing how variables relate to each other. Bayesian belief networks are examples of such models. Networks which include both discrete and continuous variables are known as mixed graphical models. The application of Gibbs sampling to mixed graphical models allows estimation of not only marginal probabilities but also means, variances and marginal densities of continuous variables, A standard model is introduced with continuous variables having conditional Normal distributions and linear relationships amongst the variables. The simulation procedure is described for this model, and then extended for models having quadratic relationships or Gamma conditional distributions. Such more general models are shown to require a hybrid strategy to generate values from the Gibbs sampler. Two hybrid strategies are described and then applied to an example for comparison.